# QM binding energy and reflection coefficient

1. Oct 10, 2008

### Felicity

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

consider a potential given by

V(x) = infinity x < 0
= 0 x > a
= a negative function of x in between

suppose it is known that the interior wave function is such that

(1/u) (du/dx) at x=a = f(E)

a. what is the binding energy of a bound state in terms of f(Eb)?

b. Suppose f(E) is a very slowly varying function of E so that we can take it to be a constant. Calculate the reflected amplitude R(k) in terms of f if the wave function for x > a has the form
e-ikx + Reikx, and check that

(the absolute value of R(k))2 = 1

2. Relavant equations

k2= 2mE/hbar2

3. The attempt at a solution

a. to find the binding energy I calculated f(E) by taking u at x > a to be Teikx so that
1/u du/dx = ik

I know that the bound states are discrete solutions where E < 0 and that in order to find them I must match the u at x > a to u in the well at x = a but how do I do this if I don't know the equation for u in the well?

b. How can the wave function at x > a be e-ikx + Reikx?

why is it important that f(E) be a constant?

where do I start?

Thank you,

Felicity