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1D schrodinger equation problem - Lozmaster - 2010-11-09
Firstly: I don't want the actual answer given to me, at least, not immediately, I would prefer if I could get hints in the right direction, or point out if i've done something stupid (normally I'd ask someone in the university, but the lecturer for the module is out of the country, and my tutor isn't responding to e-mails...), plus its reading week so everyone else on my course has gone home for the week.
For a particle mass m, total energy E < 0 in a potential V(x), where alpha is some positive constant, hbar is the wave number, N is some normalization constant
V(x)=infinity otherwise
(Thats supposed to be hbar, couldn't find a better icon for it)
Show that
is a solution of the time indep schrodinger equation (TISE) when x>0, and find the associated total energy eigenvalue E.
Now, the method I've gone for is substituting the forumla for psi(x) into the TISE,
differentiating it with respect to x for one part, and if my math is right I end up with
Anddd now I'm lost, at this point, I think I'm supposed to prove thats a valid equation for E in this situation (we were the last time this sort of thing came up), but I'm really not sure how to go about it. Unless I made a really stupid mistake, and my E is wrong, which would make sense as to why I can't verify it
Edit: I think I've got it, hopefully.