Talk:Materials in Electronics/Confined Particles/1D Finite Wells

This article had several mistakes, and has a lot to be improved:

I've corrected\added the following:

I mentioned that this is a symmetric finite quantum well. This has some unique features (which I have not yet mentioned) such as the existence of a bound state for any well depth, and the fact that the solutions can be chosen at an even and odd basis.

The definiton of V(x) was wrong (I corrected it).

The section about unbound states was completely wrong. There was no mention of the fact that unbound modes are doubly degenerate continuum modes i.e. any energy is allowable (unlike the bound states). This was even proved mathematically based on wrong assumptions on the meaning of an even/odd mode. Also the author was not carefull about when sin equals zero and did not treat that case seperately.

The previous writer wrote "An unbound state must still adhere to parity laws, so we will still have odd and even wavefunctions",

The above is wrong because of the degeneracy. Thus one can take combinations of even and odd modes which do not adhere to parity laws. The correct way is to say that because Parity and the Hamiltonian are commutative (The potential is symmetric), a basis can be found in which the eigenmodes bound and unbound states are even and odd functions. This does not mean that this is the only basis!

Eran 4/7/08

Future Changes
I changed the unbound section so it has no mistakes (To the best of my knowledge), but I'm sure it could be improved much further, by showing sample solutions of continuum modes and expanding the section about the resonances where the anplitudes above the well become very high.

The modes need to be normalized.

I think the page could be ameliorated by noting the relation of the potential well to optical waveguides and Fabri Perot resonances (Constructive interference).

Eran 4/7/08