In Search of Schrodinger's Dice
- Thread starter FyreStar
- Start date
einsteinsdream
Registered Member
Richard Feynman's "sum-over-paths" approach to quantum mechanics assigns numbers to the possible paths that particles (electrons, for example) can travel in such a way that their combined average yields exactly the same results for probabilities calculated using the wave function approach.
I don't know if this answers your question but I think it puts you on the right track.
See Brian Green's "The Elegant Universe" and Timothy Ferris' "The Whole Shebang" for further explications.
I don't know if this answers your question but I think it puts you on the right track.
See Brian Green's "The Elegant Universe" and Timothy Ferris' "The Whole Shebang" for further explications.
Hi Fyrestar,
In "classical" quantum mechanics, they are not quantized (as fas as my knowledge of QM goes).
If they were to be quantized, then this would imply that the probability for finding a particle somewhere would also be quantized, and this seems like a rather odd result to me (in regular wave mechanics).
You could say that when you measure the particle's position (and have a collapse of the wave function) that the wavefunction is quantized for a very short time: when meaured, you know the exact location of the particle, and you know that it cannot be anywhere else. Hence you have only one allowed position, and a lot of forbidden positions, just like you would have allowed energylevels and forbidden energylevels (even though the "allowed" positions grow rapidly as time increases).
However, I don't think this can be counted as a quantization (since "regular" quantizations are not time dependant for isolated systems) so I think it's pretty safe to say that wavefunctions are not quantized.
Please prove me wrong if you know an example where they happen to be quantized
.
Bye!
Crisp
------------------
"The best thing you can become in life is yourself" -- M. Eyskens.
[This message has been edited by Crisp (edited January 18, 2001).]
In "classical" quantum mechanics, they are not quantized (as fas as my knowledge of QM goes).
If they were to be quantized, then this would imply that the probability for finding a particle somewhere would also be quantized, and this seems like a rather odd result to me (in regular wave mechanics).
You could say that when you measure the particle's position (and have a collapse of the wave function) that the wavefunction is quantized for a very short time: when meaured, you know the exact location of the particle, and you know that it cannot be anywhere else. Hence you have only one allowed position, and a lot of forbidden positions, just like you would have allowed energylevels and forbidden energylevels (even though the "allowed" positions grow rapidly as time increases).
However, I don't think this can be counted as a quantization (since "regular" quantizations are not time dependant for isolated systems) so I think it's pretty safe to say that wavefunctions are not quantized.
Please prove me wrong if you know an example where they happen to be quantized
.Bye!
Crisp
------------------
"The best thing you can become in life is yourself" -- M. Eyskens.
[This message has been edited by Crisp (edited January 18, 2001).]
Hi Epitectus,
I don't immediatelly see a reason to use galactic coordinates (arent these plain regular spherical coordinates anyway ?) in the Schrodingerequation, but if you like, then you can use them yes.
All you need to do is express everything in terms of these galactic coordinates; you'd have to evaluate the Laplace operator in these coordinates, and express the potential in these coordinates aswel.
I don't think anyone has done this before, but since you're always free to choose your base of reference and your coordinatesystem in classical quantummechanics I'd expect no problem.
Bye!
Crisp
------------------
"The best thing you can become in life is yourself" -- M. Eyskens.
[This message has been edited by Crisp (edited January 30, 2001).]
[This message has been edited by Crisp (edited January 30, 2001).]
I don't immediatelly see a reason to use galactic coordinates (arent these plain regular spherical coordinates anyway ?) in the Schrodingerequation, but if you like, then you can use them yes.
All you need to do is express everything in terms of these galactic coordinates; you'd have to evaluate the Laplace operator in these coordinates, and express the potential in these coordinates aswel.
I don't think anyone has done this before, but since you're always free to choose your base of reference and your coordinatesystem in classical quantummechanics I'd expect no problem.
Bye!
Crisp
------------------
"The best thing you can become in life is yourself" -- M. Eyskens.
[This message has been edited by Crisp (edited January 30, 2001).]
[This message has been edited by Crisp (edited January 30, 2001).]