QM: Potential Well

1. Sep 28, 2008

bobcat817

1. The problem statement, all variables and given/known data

An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube). Specifically, the proposal is to build a well with L = 1mm, inject some electrons into it, and then measure the wavelength of photons emitted during low-n transitions via optical spectroscopy. As an expert on quantum mechanics, you are asked to evaluate the proposal. What is your recommendation?

2. Relevant equations

E = $$\frac{\pi^2\hbar^2}{2 m L^2}n^2$$

$$\lambda$$ = $$\frac{h c }{E}$$

3. The attempt at a solution

Questions: Can electrons transition without a nucleus? Is it responding to some nucleus outside of the well? Does it have nothing to do with nuclei at all? What exactly are low-n transitions?

I'm very confused, so any direction would be appreciated. I know that the proposal should be refused, but I don't know why. By playing around with the equations above, I though perhaps that the wavelength wasn't in the visual spectrum, but I'm not sure that combining the two equations even makes sense.

2. Sep 29, 2008

olgranpappy

you can take "low-n transitions" to mean n=1 or 2 or so. That is, plug in n=1 or 2 or whatever to the 'E' formula and find E. Then plug that E into the '$\lambda$ formula and find $\lambda$. Compare the wavelength you find to the wavelength of visible light.

3. Sep 29, 2008

bobcat817

Thank you very much. That's what I did initially, but I wasn't sure if that was the right method.