Shape of standing wave

Discussion in 'Chemistry' started by quantum_wave, Dec 22, 2012.

  1. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Just a quick question: Looking at orbitals and their various shapes and energies, and looking at the layman level chapter in an old (2000) chemistry book in the sub-chapter on Wave Properties of Matter and Wave Mechanics, they are getting into electrons as standing waves right after they briefly mention Erwin Schrodinger on the wave nature of matter. They quickly say, "... His work and the theory that developed from it are highly mathematical. Fortunately, we need only a qualitative understanding of electronic structure, and the main points of the theory can be understood without all the math."

    They characterize the orbitals at a given energy to be calculated using the wave function, and they refer to the shape of the electron wave and its energy. Does the "shape" of an orbital refer to the three dimensional space within which, according to probabilities, the particular electron can be found relative to the nucleus when the atom is at a certain level of excitement and will remain within that unchanged space until an energy change within the atom occurs (which in practice, I suspect, change occurs in the next instant, lol.)?

    And about the standing wave nature of the electron: is the shape of the orbital while it has that particular shape and energy said to be a standing wave, and does that mean that the wave is two dimensional and in its natural action within that orbital can be anywhere within that three dimensional space? Or have I gotten off track on thinking this through?

    Edit: What I'm getting at with the standing wave question is the discussion in my most recent Chemistry book, in the Chapter about Atomic and Electronic Structure, refers to the electron in particular as a standing wave, but in general I take the discussion about standing waves to be referring to matter waves in general being standing waves. I guess I could ask, does the quantum mechanical model of the atom that uses orbitals (which are referred to as standing waves) for the electrons, also refer to the quarks in the nucleons as standing waves as well?
    Last edited: Dec 22, 2012
  2. Google AdSense Guest Advertisement

    to hide all adverts.
  3. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    I did a search for "Are quarks standing waves", and this far out link came up:

    Looking at the variety of links in that search, I can't tell what is the generally accepted quark theory. Does anyone have a link to what is said to be the consensus quark theory or are there many that share the spotlight?

    This is an interesting link on the topic: quarks standing waves&f=falsec
    dating back to 1987 from a book called the Great Design, Particles, Fields, and Creation (hmm)

    But anyway, there are multiple sources in that search that refer to quarks and electrons as standing waves, so unless you object, let's refer to them as standing waves.
  4. Google AdSense Guest Advertisement

    to hide all adverts.
  5. Aqueous Id flat Earth skeptic Valued Senior Member

    The shape of an orbital is the zone in which the electron (treated as a particle) is said to exist with probability=1, given that it exists at any particular radius and time as the wavefunction Ψ(r,t). These orbital zones can be arrived at by integrating the wavefunction over volume, and setting the result equal to 1. (The sum of the probabilities is equal to 1).

    Upon solving in spherical coordinates, you get, for each combination of quantum numbers, the equations which describe these shapes. Here you find tabulated the various solutions for each case. Also see slide 3 here.
  6. Google AdSense Guest Advertisement

    to hide all adverts.
  7. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Interestingly, my chemistry book, "Chemistry - Matter and Its Changes", Brady, Russell, Holum, 2000 edition, covers that material better than my most current physics book, also a 2000 edition, "Physics For Scientists and Engineers Fifth Edition", Serway and Beichner. I am not interested in confirming the math, only in understanding the principle behind the wavefunction and quantum numbers as they are used to define the orbitals, and I may be wrong but I doubt if very many layman would want to try to develop the math necessary to show the orbital configurations for all of the energy levels of even the simple hydrogen atom that correspond to the Rydberg equation that gives the spectral lines. I wonder, does the Rydberg equation apply to all atoms and spectral lines?

    And to those who can contemplate such a task I direct my next question:

    Does the current quantum mechanical model of the atom with the orbitals calculated using the wavefunction,
    and the quantum numbers, yield results that correspond to the full range of energy levels that cover all of the absorption lines of light by all of the atoms in the periodic table as given by the Rydberb equation, i.e. can we create an orbital configuration for every spectral line of all atoms, and is it an elegant calculation?
  8. Aqueous Id flat Earth skeptic Valued Senior Member

    Understanding orbitals is a basic principle in chemistry, which is why you would see it covered in a intro level chem book. Intro to Applied Physics usually covers statics and kinematics first, since those are prerequisites for courses in engineering and applied sciences.

    The links I gave were intended to explain the principles. It's impossible to explain the derivation of orbital shapes from the wavefunction without doing the derivations, which requires a little math. I can walk you through it verbally:

    Consider the wavefunction Ψ(r,t), which gives the probability that an electron is present at radius r at time t, within the boundary [0, L]. The sum of all of these probabilities over the volume is 1. Therefore, by integrating Ψ(r,t) over volume, and setting it equal to 1, we can solve for the values of r and θ (radius and angle) for each point along a vertical axis Z. The solution will yield the specific orbital shape to which a particular electron is confined, in cylindrical coordinates (r, θ, z). Furthermore, it can be written in terms of the quantum numbers for each energy level.

    (This is one of several approaches.)

    Few non-technical people have any clue what you even talking about. I only offered it since you asked. All you need is a passing knowledge of Calculus and Probability Theory. It would help to have some idea of what a wave function is, what it means, and a little wave mechanics in general. A little trig, too. And it helps to understand some of the properties of the exponential function. Other than that its just a matter of plugging a few pieces together. If you are interested in exploring this more, I'd be glad to help. As for what non-technical people might want to do with this information, I think it would interest the curious ones more if they understood the profound implications of it.

    that's the easiest part, if we follow the scheme above, since we account for each energy level by solving for each combination of quantum numbers corresponding to each energy level.

    Not sure what you mean here. Are you wanting to compare orbitals and spectra? What sort of connection between them did you have in mind?

    Keep in mind there is one wavelength for each step size in energy transition. As soon as you say "spectrum" you are describing the aggregate summation of all atoms in an actual physical sample. Rydberg won't cover much ground, and it will only give you an idealized result. Also note, the basic Rydberg formula applies to atoms having only 1 electron (hydrogen and a few ions).

    Let me try to break that down.
    The only model we started with was the wavefunction. The orbitals arise directly from this. This pales in comparison to the modeling used to estimate spectral lines accumulated across countless atoms randomly jumping up and down in energy, as in an actual lab sample or telescope image.

    (and the quantum numbers representing the energy level of each)

    "Full range" might be ambitious. You might want to start from a more basic position, constructing a simple table of atoms in the ground state and easing into the more complex configurations slowly.

    One energy jump gives you one line. A higher (positive) jump gives you a higher frequency (lower wavelength). As soon as you mention spectra, you exit the realm of idealization and moved into the lab or observatory where you have an actual sample of countless atoms jumping a random number of energy levels. The aggregate of all possible lines becomes superimposed. But interpreting data can be problematic, too. So it may be difficult to put all of what you just said into a lucid statement of a goal.

    No, it only applies to Hydrogen and ions with one electron. A better approach might be to find or create a simulation that works all of this out for you. But you will have your hands full trying to set up a "full" simulation. That is, you would have to enumerate all the assumptions your simulation makes, and program for them (i.e., zero scattering, pure homogeneous material, etc.) What you're asking could be arrived at incrementally if you had to try to do it from scratch, because that's the only way you'll begin to get a handle on all that's implied in the question. If you were to adjust your expectations downward, however, you could fairly quickly arrive at the simpler idealized scenario. It just may be disappointing if you were hoping to cram a lot of complexity into a simplification.

    I think the best you can do is to create a collection of all the feasible electron configurations, and to collect (or calculate) the orbital shape for each, and then to calculate the idealized wavelength for each, and the various spectral series predicted according to whichever estimator you settle on (or just pick Rydberg for the heck of it). I would say that the calculations are simple and straightforward. But you will get a list of apples and oranges since they are two entirely different things. The orbital is a 3D region of possible occupancy by the particle and the wavelength (or frequency) is its corresponding energy. It's a useful thing to do, to familiarize yourself with principles, but I would recommend starting with the scheme for generating the quantum numbers, and to learn why the wavefunction produces these specific shapes. Also it might be helpful to collect some of your ideas/hypotheses about how/why these two parameters (orbital, wavelength/spectra) relate. Finally, you would probably need to treat the question of spectroscopy, and the particular issue of what measured data actually means. But the easiest of ideas is the way frequency is calculated. It's simply the energy divided by Planck's constant; one freq for each delta in energy.

    Also: most practical scenarios only deal with a jump up or down 1 or 2 levels by the outer electron. If you go looking for every possible way to ionize an atom for every atom in the periodic table, you're going to create a large number of unrealistic and/or impossible scenarios, and then you'll have to come up with a way to mull each case over and create a rule for what to leave in and what to leave out. For this reason you would probably want to start off with a small and simple way to formulate the question and then work your way towards complexity gradually, as the principles become more familiar and easier to wield.
  9. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    That is good to know. I pickup text books on all of the sciences when I see them for a few dollars for books that may have cost fifty or a hundred dollars new. That explains why my library is ten or fifteen years out of date, lol. But I do have the Internet and the library is walking distance so I have access to pretty current science, it is just knowing where to look. I'll be looking closer at my chemistry books for awhile while I pursue my current line of study.
    The links you gave me were good, and as I look at my text books and the Internet searches I have done, they are familiar. And I appreciate your time in explaining the derivation of the shapes of the orbitals given the boundary conditions. Do the quantum numbers define the boundary conditions? And then using the wavefunction and the quantum numbers, leads to a specific solution for the orbital of a specific electron, giving us the "shape" of the space within which the electron will be with 100% probability?
    We seem to have at least some common ground in the context of this thread and this forum, so I'll take advantage of your offer and ask a few questions about it: How do you make your keyboard show the Greek character for the wavefunction? Do you have to switch fonts or use LaTeX?

    You probably know that I could go to my texts and the links you gave and work through an example or two and get a good idea of the process, and you may be able to tell that I hadn't intended to do that because getting the concept was going to satisfy me; so your being willing to help would result in a combination of you pulling me along and me going at a very slow pace compared to the pace I could go if I exercised the intuitive to work a few examples on my own. I would think that you might see that as a waste of your time, but it would result in me doing it when I hadn't intended to. Let's leave it that I could come back to this forum and thread and probably get your help if I decided to do it later, which has some level of probability, but not = 1,

    Please Register or Log in to view the hidden image!

    I am vaguely familiar with what they call the Aufbau Principle for imagining the electron structure of multiple electron atoms. Given the theoretical pairings and exclusions as we build up and fill out the successive rings by applying Hund's rule and the Pauli exclusion principle.*
    The common ground I speak of with you is that there are observations from experiments like the Rydberg constant that give us the departure point, and beyond that observational departure point there is theory; the theory is the mathematical description, and the peer review and general acceptance of theory is what I would call the current consensus. It may be right or it may be wrong which is to be determined by confirmation of proposed tests and experiments and hopefully better observational tools. It is the observations that will move the theory to observational fact. The spectral lines of emission called the emission spectrum are where the Bohr model of orbiting electrons breaks down after Hydrogen, according to my texts.
    There, we have the answer to my question; the Rydberg equation is limited in that respect.
    Maybe we need to be practical when it comes to what the wavefunction and quantum numbers can do, and what they are best at doing. They are best at conveying the theory of the nature of the orbitals and they are limited when it comes to building exact mathematical configurations for each emission line that a multiple electron, multiple layer atom may show in its emission spectrum; that would be logical to say, I think.
    Good advice. I like going back to observational departure points like Planck's constant. I see some correlation between Rydberg's constant and Planck's constant, at least to the extent that they are confirmed observational data. There is probably more of a connection that someone more familiar than I am could see.
    True. When I first posted this thread I made reference to Erwin Schrodinger and his concept of the wave nature of particles and the electronic structure. How directly related to the Schrodinger equation is the wavefunction and the quantum number explanation of the structure of atoms?
    Last edited: Dec 27, 2012
  10. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    I replied to this thread almost 24 hours ago and it still hasn't posted.

    Now I see it and it posted before this post, so maybe it was there all the time :shrug:
    Last edited: Dec 27, 2012
  11. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Electrons and quarks as standing waves

    No one has objected to my reference in the above post that electrons and quarks are described as standing waves in quantum mechanics. I'm hoping for some discussion to follow and so I offer the following discussion starter:

    Electrons, quarks, and therefore protons are characterized as standing waves in quantum mechanics, and electrons and quarks are charged particles. (Neutrons of course, also composed of quarks, have a neutral charge based on the sum of the fractional charges of the types of quarks that make them up, but in the nucleus of the atom, all of the fundamental particles are charged.)

    Is it safe to say that the charge of those particles must be a characteristic of the standing waves and/or a characteristic of the way those standing wave particles influence each other given their relative motion? For example, is it the interaction between them that establishes the charge (since acceleration causes electromagnetic radiation that results in electric and magnetic fields)?

    Can someone discuss the characteristics of those standing waves and/or the interactions between them and how that establishes or determines the charges of each of the fundamental particles in an atom? If an electron is confined to the volume of the particular orbital determined by the wavefunction and the quantum numbers, would the motion of the electron within that orbital space determine the shape of the fields generated by its motion, and how could that determine the individual particle charges?
  12. AlphaNumeric Fully ionized Moderator

    All particles are described by wavefunctions. The shape of the electron orbitals are determined by the charged interactions between electrons and nuclei, so in that case the orbitals depend on charge. Any particle in a box on its own will have a wavefunction so it isn't like you have to consider charged particles.

    The orbitals in atoms are defined by the energy eigenvalues of the Schrodinger operator. The electron energies can only take certain values and the orbitals are all distinguished by their energies and spin orientations. The orbitals do not interact, they are not things. The electrons and protons interact and the orbital is the resultant behaviour of an electron in the atom. The 'orthogonality' of the functions follows mathematically from the structure of the Schrodinger operator; Hermitian means Real (no imaginary numbers) eigenvalues and the eigenstates are orthogonal with respect to the Sturm-Liouville inner product (if doing things in terms of functions, not bra-kets).

    The reason we can talk about orbitals, these 'pure' configurations, is the Schrodinger operator in question is linear so any general solution is formed by the linear combination of these 'pure' states (eigenfunctions with the associated eigenvalues). The way in which the state of a particle is described by a wavefunction varies in time, as different energies means different time evolutions but it is always a combination of the pure states.

    For non-linear Schrodinger systems this doesn't occur, you cannot talk about the pure states in the same way.
  13. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    OK, so charge is a characteristic of the particle, and the model of the atom we are using is useful because it employs orbitals. The mathematical calculations that result in the shape of the orbitals use the wave function and the quantum numbers, and the resulting orbital patterns are abstract mathematical representations that are meant to reflect the charged interactions between the electrons and the nuclei. This is useful in QM so that the experiments and results can be described mathematically and in a way that is consistent with the purpose at hand? Is that anywhere near close?
    So the wavefunction can be noted in bra-kets or functions? I'm not sure I understand that at all but don't try to explain, I'll look it up in Wiki when I come to it, before I ask for help with it

    Please Register or Log in to view the hidden image!

    Again, I can't help but fall back on the idea that our descriptions of particles depend on the model we are using and on the nature of what we are trying to accomplish, or what one of the texts I have refers to in terms of their "usefulness" and not their "truthfulness". I'm certain you don't take that as some criticism of QM, and it's not. The nature of the mathematics employed in QM is abstract and theory dependent, and the tools used are numerous and chosen by the objective. Is that anywhere near close?

    But I am picking up that the Schrodinger equation deals with change over time, so if that is right, it might answer the question I posed to Aqueous ID earlier.

    Thank you both for the help. I'll conclude that the standing waves reference I picked up from my old texts and from Internet searches are more of a description in the context of particles (and objects composed of particles) being described by wavefunctions. I also can conclude that the charge of particles has nothing to do with the interaction between particles, but instead are characteristics of the particles themselves, and the particles themselves are generally defined by observations of particles, particle interactions, and various mathematical models that are useful in different circumstances to set up experiments and measure results?
  14. Aqueous Id flat Earth skeptic Valued Senior Member

    I picked this since it was the quickest to answer. I was off in the hinterlands and didn't get around to a timely reply to the rest of what you said on the the 25th. I used Character Map (windows: start → run → charmap) to generate Psi (Ψ).

    I use the character codes for some of the off-keyboard characters, which encode as standard ANSI. For example the degree mark ° is ALT-248 in Windows (decimal), and so on. You can access Unicode in script by for example &_#8594; encodes a right arrow. (Omit the underscore).

    A few of these I just happen to remember, from back when that was important. Sometimes it's easiest to just pull up charmap.exe and pick a symbol from the app, copy and paste. Most LaTex I do is with the Datum Equation Editor freeware I have installed on my browser. In most cases it's faster and easier for me to use than coding. I flip over to it when I want to spell something out, build the expression symbolically--then the app gives the script to insert in the post. Just copy and paste. Even faster is to lift an equation as an image (say from Wikipedia) and copy and paste. For inline coding of sub and super scripts I use the coding explained the site FAQs: [*sub]n[*/sub] and [*sup]n[*/sup] (without the stars, or you wouldn't see it). e.g. 2H[*sup]+[*/sup] + O[*sub]2-[*/sub] & #8594; H[*sub]2[*/sub]O (without the stars) will encode: 2H[sup]+[/sup] + O[sub]2-[/sub] → H[sub]2[/sub]O. (Or copy and paste the arrow from charmap). It's almost as messy as LaTex, and only works for simpler notation, whereas LaTex conquers just about everything. But for a small thing like Psi, I would grab it from charmap. If I had to recreate the expressions Alpha used above I would use my Equation Editor.

    I would say it differently. I would say that quantum numbers and the wavefunction define certain laws about how atoms work. Were it not for these laws, the periodic table would be different, copper might be an insulator, and life forms might be Boron-based rather than Carbon-based. I wouldn't tie them directly to describing the nature of orbitals, since that's essentially a model. The true nature of the quantum world will always hold certain mystery, so we are stuck with modeling, since there is not always a meaningful way to translate quantum world properties and principles to the ones we experience in the real world.

    I think peer review and consensus has more to do with scrubbing a proposition for accuracy before declaring it a settled matter, primarily to save future investigators the effort of having to redo every piece of work upon which the proposal depends. It also ensures that few reports will later have to be withdrawn for sloppy work. In consensus building, everyone wants to be assured that everyone else hasn't found a flaw because they themselves haven't either. Having wide participation also ensures that results are repeatible under every scenario that needs to be tested.

    Bohr knew about energy quantization, but not the wavefunction, so he reasoned that discrete concentric spheres was the correct model. As it turns out that's not too bad for Hydrogen, since just a single electron is involved, and its lower levels are spherical, as in the Rydberg model. But the fact that it broke down elsewhere also leads to the connection from Rydberg and Einstein to Bohr/Heisenberg/de Broglie, leading to a fusion between Rydberg's early model, Bohr's link to Einstein's photoelectric effect, and the wavefunction. It was a process of evolution.

    Since Hydrogen only involves one electron jumping levels during transition, and since the lower shells are spherical, the Bohr model was reasonably close. The wavefunction-Rydberg hybrid accounts for the eccentric shapes of the higher orbitals but still is idealized to a single electron jumping through them. Further, unless a model accounts for everything that goes on in a clump of mass under spectroscopy, the aggregate behavior deviates from the idealization. Molecular level interactions, scattering, doppler, etc., aren't in the simplified model, nor are some systemic effects, so to some extent it's apples and oranges. (This leads to a discussion about spectroscopy.)
  15. AlphaNumeric Fully ionized Moderator

    The model leads to orbitals, which are experimentally observed. This is an example of a physical manifestation of a very formal mathematical construct. The Schrodinger operator, which governs the dynamics of the system, is an Hermitian linear operator, meaning it has real eigenvalues and orthogonal eigenstates. The eigenvalues are the mathematical representation of the energies of the orbitals, which are the physical manifestation of the eigenstates. These are the 'special' states. If a system starts in a combination of some particular set of states it will ALWAYS be in that particular set of states, though the precise combination will vary in time. This means if a system starts in a pure orbital then it will never move to another orbital. However, if the wavefunction is a combination of the orbitals then the time evolution due to the operator tells us how to work out the probability of changing orbitals.

    It derives them. The quantum numbers are the indices which define how we label the wave function eigenstates.

    Pretty much, the orbitals are the configurations which only map to themselves under time evolution. For example, if the wavefunction is a combination of orbital 3 and 8 then it will always be in a combination of orbitals 3 and 8. The 'orthogonality' means that there is, mathematically, no overlap between the orbitals. Any overlap between a wavefunction and an orbital means there's a possibility the particle is in that orbital. For Hermitian operators they are always orthogonal so if in a combination of orbital 3 and 8 then there's zero change it is in orbital 6. For non-linear systems or some of the more wacky quantum extensions (typically all operators of physical relevance are Hermitian so have orthogonal eigenstates) there can be a non-zero overlap, hence why they are more complicated to model, the particle could jump all over the place.

    Yes, quantum mechanics is perhaps one of the best examples of how abstract mathematical structures can actually 'manifest' in the real world. It occurs everywhere else but not with such a nice clear cut way.

    Bra-kets are a way of representation vectors. Quantum mechanics is perhaps the best area of physics for seeing how it is possible to describe the same system in many different ways.

    No, if anything good physical models have built into them an invariance in our abtraray choice of things. For example, relativity doesn't care which inertial frame we pick, as that is not a physically meaningful choice. Some representations make it easier to compute certain things but in principle if two representations are equivalent then you can compute exactly the same things in each.

    This is seen in the gravity-gauge duality known as the holographic principle. It is horrific to compute QCD processes involving mesons in a temperature bath using gauge theory. Using the duality we can write the system in terms of gravitational fields, which we can compute in till the cows come home. We then convert our answer back into the language of gauge theory and there's the result. In this way it is 'easy' (read as 'mind warpingly difficult but less difficult compared to the direct way') to compute things about nuclear superconducting flows, something otherwise beyond our abilities using supercomputers and QCD.

    Physics is the science of writing difficult things you don't know in terms of simpler things you do. In some cases the change of representation means you are making an approximation or you're throwing away some information in order to get at the information you want. Provided you know the limits of your approximations and remember to put back the information you threw away when it is relevant this is okay.

    A simple example is modelling populations using predator-prey examples. The populations are obviously whole numbers, you can't have half a rabbit or 0.84 foxes, yet it is common to model populations using differential equations, which can give non-integer values. Provided the populations are very big their behaviour is essentially smooth and the differential equations are accurate. If the population is small then they are nonsense, you can't model the population changes of half a dozen animals using differential equations.

    A more complex examples is gauge fixing in field theory. How you describe a particle field has a massive amount of redundancy if you use gauge theory, much like relativity has the choice of a frame. To do an explicit calculation you must fix the gauge, which often has the weird effect of introducing 'fake particles' (known as 'ghosts') due to this redundancy reshuffling the fields. You have to treat them carefully and you can't then use your results to apply to a different gauge calculation but two people calculating physical things like scattering of particles should get the same result, regardless of which gauge they pick. Up until they compute the physically observable thing they might have wildly different mathematics but they obviously must agree on the measurable stuff. This applies to renormalisation too, its got a lot of arbitrary choice in it but it all evaporates off in the end. This is why it isn't just slight of hands with infinity, it works.

    Always in physics it is a matter of using the right tools for the job. Two people asking different questions of a quantum mechanics system will do different things but it all flows from the same original construct, which has built into it as much machinery as possible to remove issues of arbitrary choice.

    The Schrodinger operator, the time dependent one, is (up to signs I might not remember right) \(i\partial_{t}\psi = H\psi\), which is solved as \(\psi(x,t) = e^{iHt}\psi(x)\) (this is a vector expression and \(e^{iHt}\) is the exponential of a matrix not a number!!!). If you work in the eigenbasis you get \(\psi(x,t) = \sum_{n}c_{n}e^{iE_{n}t}\psi_{n}(x)\) where the \(E_{n}\) are the eigenvalues/energies, \(\psi_{n}\) the eigenfunctions/orbitals (for atoms), \(c_{n}\) some and \(n\) indexes the orbitals/eigenfunctions. The energies control how the phases of the orbitals vary. A single phase is irrelevant but when you have a combination of orbitals the energies control how the system moves around them.

    See, good questioning leads to good discussions

    Please Register or Log in to view the hidden image!

    The charges are what lead to the orbitals, as they hold the electrons around the nuclei, but the orbitals themselves do not interact with one another like particles interact with one another. The orbitals are highlighted regions of space where particles might be found and which, as I explained, have particular properties pertaining to the Schrodinger operator.

    Yes, the difficult part is you cannot probe an orbital, it is just a region where a particle might be found, so you have to look at where electrons are in lots of atoms. Except you can't see the electrons directly, you have to bounce light of them, which you then detect using some piece of equipment. So all the raw information is just blips in electrical circuits. So you need a model which tells you how those blips relate to returning light and how the returning light interacts with the particles you are interested in (and the particles you aren't interested in!).

    To go on a slight tangent this is why I dismiss Sylwester's work. The values for things like the size of a proton, the value of Planck's constant, the decay width of a Strange quark, are all found by using mainstream models to link the blips in the electrical circuits with the internals of atoms. If you dismiss those models then you cannot trust any of the values they have been used to derive, you have to go back to the raw data and use your own models of how the blips relate to light, how light relates to particles, how those particles relate to one another and then you compare your predictions with the processes data. If QCD is wrong then not only might the value of the strong coupling constant \(\alpha_{S}\) not be about 0.1, it might not even have a meaning, there might not even be a strong force!

    The work required to convert raw data into something as simple as the mass of a new particle is staggering. And I don't pretend to know how you even start designing a 27km, 10 billion dollar superconductor to facilitate that.
  16. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    FAQs: x[sub]n'[/sub] and y[sup]-n[/sup]

    Cool, thanks for the simple instruction for sub and super scripts. Would there be other simple codes in the FAQ, and is that a SciForums FAQ?

    And since I am almost exclusively posting from iPad or iPhone and trying to let my old, slow PC gather dust, I don't always have the character map from Windows. I haven't checked the app store yet but I bet I could find a good app if I start to use character codes and don't want to bother with images of them.

    I don't have much call for LaTex for equations but I have used it on occasion; there is probably a LaTeX app too, lol.
    Excellent instructional comments that make sense. I know the first one is free, but do you start to charge for these short cuts to enlightenment after a few samples, lol.

    As you can tell, I'm struggling with the spectral lines and the ability to model atoms in such a way that they show what frequencies will be absorbed and emitted. It is certainly something that the photoelectric effect must involve to some degree. That effect is one of the observables that account for the consensus wave-particle duality of photons. I just cannot get it through my head how a particle can be composed of anything buy waves. Can you enlighten me on that for free

    Please Register or Log in to view the hidden image!

    . When a photon is observed as if it was in a particle state, and we can measure the energy of that frequency using e=hf, how do we describe that photon in a way that distinguishes it from its wave state?
  17. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Thanks, and I trust all that is essentially true, and it is helpful.
    I don't think we have gotten into a good discussion but perspective is everything. From my perspective I come to a question and ask it, and from you perspective you answer it. I just don't want to have to go to Wiki ten times to understand your side of the discussion. That is not a criticism, it just acknowledges that you are better at communicating with science and math professionals than with laymen who are science enthusiasts. Don't stop trying though, and don't feel that I am asking you to instruct me on how to overcome my shortcomings if you can help it, I know they are many. And I do use more sources than just Wiki; it is just that I have been told often enough that Wiki is a dubious source and so mentioning it puts my level of expertise into the perspective, lol.
    Good point, and I get it.
    That was off on a tangent. I don't follow his work but I'm sure your perspective on it is generally accepted among professionals.
    Now that is something we have in common.
    Last edited: Jan 1, 2013
  18. river Valued Senior Member

    How though do we picture the , standing wave ?

    I myself pictured this wave , as a three dimensional ocean like wave that continuously moves around the object
  19. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    A standing wave particle in QM is hard to visualize, but that is not the way I would describe it. You can Google it and get some images like I linked to in post #2, and you can also review the video clips that are also linked in that post if you want to visualize something, but I think visualizing a standing wave electron that is modeled in QM would look more like the orbitals that Aqueous Id liked us to in post #3.
  20. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    What I want you to tell me (confirm) is if it is true that atoms do absorb and emit radiation of particular wavelengths, and that atoms of the same element will absorb and emit radiation of the same frequency when at the same energy levels, giving them each a "signature" in the light spectrum when it is analyzed by the absorption and emission lines in the spectrum of their light. Then I want to know if we have a way to model an atom, each atom, at each level of energy, regardless of how difficult the math would be or how much computer power we would need, that will allow us to derive what the frequencies will be of the specific spectral lines in the light absorbed and emitted by those atoms.

    So here is a link to Wiki on spectroscopy:
    Atomic spectroscopy was the first application of spectroscopy developed. Atomic absorption spectroscopy (AAS) and atomic emission spectroscopy (AES) involve visible and ultraviolet light. These absorptions and emissions, often referred to as atomic spectral lines, are due to electronic transitions of an outer shell electron to an excited state. Atoms also have distinct x-ray spectra that are attributable to the excitation of inner shell electrons to excited states.
    Atoms of different elements have distinct spectra and therefore atomic spectroscopy allows for the identification and quantitation of a sample's elemental composition. Robert Bunsen and Gustav Kirchhoff discovered new elements by observing their emission spectra. Atomic absorption lines are observed in the solar spectrum and referred to as Fraunhofer lines after their discoverer. A comprehensive explanation of the hydrogen spectrum was an early success of quantum mechanics and explaining the Lamb shift observed in the hydrogen spectrum led to the development of quantum electrodynamics.
    Modern implementations of atomic spectroscopy for studying visible and ultraviolet transitions include flame emission spectroscopy, inductively coupled plasma atomic emission spectroscopy, glow discharge spectroscopy, microwave induced plasma spectroscopy, and spark or arc emission spectroscopy. Techniques for studying x-ray spectra include X-ray spectroscopy and X-ray fluorescence (XRF)."

    There are some good Wikies

    Please Register or Log in to view the hidden image!

    . I'm looking over the link to QED to see if I can find something on the modeling of the atom that explains the nature of the internal configuration. If an atom at a given energy state will always absorb radiation of a given frequency, wouldn't there be a model to show the configuration?
    Last edited: Jan 3, 2013
  21. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

  22. AlphaNumeric Fully ionized Moderator

    You can picture 2d systems like that, since the 3rd direction represents the strength/value of the wave. For 3d waves you cannot do that but one alternative is to use colour. Blue might mean low value and red high value. That's what the orbital pictures you'll see on Wikipedia use.

Share This Page