It is a homework question and I solved it in the following way: To Prove that (∆θ)(∆L)~(ћ/2) ;For what uncertainty of L will the angular position of the particle would be indeterminate? I considered a particle of mass m moving in a circle of constant radius r at speed v.Then,classically,L=mvr. Clearly,from uncertainty principle, ∆s ∆p~(ћ/2) => (∆s/r)[(∆p)r]~(ћ/2) => (∆θ)(∆L)~(ћ/2) What I am worried if this particular case of a circle will do;and the second question.I think it is ∆L=0 which makes ∆θ indeterminate...But I am not sure... Please check if this is correct and rectify if I am wrong.
God... I haven't done things like this in ages. Emmm - yes... ∆L=0 would make ∆θ indeterminate (I think...)
Since \(\Delta \theta \Delta L \approx \hbar/2\) it follows that \(\Delta \theta = \frac{\hbar}{2 \Delta L}\) Therefore, if the uncertainty in L is zero, then the uncertainty in theta is infinite. neelakash: Can you please use [ tex ] tags for math? The equations are easier to read that way. Quote this post to see how the above equations were produced, for example.
James R, the problem is that I cannot remember all the codes...I have tried earlier to make my equations in Latex...But I saw that different forums use different codes and what makes the thing for one forum may not be applied to some other forum. Also,it is very cumbersome to write lines of codes to make equations after equations...So,what I now do is to make a list of requisite symbols from ms Word 2007 and copy-paste them where necessary. Is there any problem to understand what I have written? I suppose not.each of the symbols are clear... Anyway, if there is any handy way to use Latex,please let me know... I will be happy to learn and apply. Regards, neelakash
There is a latex guide at the top of the forum page. I too found it a bit, difficult to sy the least. I'm used to writing equation down by hand, instead of this system...
Any forum which uses TeX will use essentially the same code. TeX (and/or LaTeX) is one of the standard languages used by professional mathematicians and physicists to write scientific papers and books for publication. Writing equations in LaTeX is not too hard to learn. Most symbols are produced by commands preceded by a backslash. For example, greek letters are produced by \alpha \beta \gamma and so on (capitals by \Alpha \Beta \Gamma etc.) The other main tricky thing is fractions. The easiest way to get a fraction is with something like \frac{x}{y} which produces x over y. The top of the fraction goes in the first pair of braces, while the bottom goes in the second pair. Superscripts and subscripts are easy, too. For example, x squared is produced by x^2, and O2 (as in oxygen molecules) is produced by O_2. The only slight catch is that if you want something like x to the power of (a plus b) you need to use curly brackets again, as in x^{a+b}.
Once you have learned the basics, Latex is by far the quickest, easiest way to make typeset equations. In most cases, a proficient Latex user can type an equation as fast as it can be written by hand. There's a good reason that it enjoys a near-total monopoly in technical professions.
