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peripatein
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Homework Statement
A particle is in the following potential:
V(x)=infinity for x<0; -V0 for 0<x<a; and 0 for x>a
Given that there's only one bound state I am asked to determine the range of values for V0 in terms of the width a and the particle's mass m.[/B]
Homework Equations
The Attempt at a Solution
For -V0<E<0 I chose the following general solution for the wave function:
ψ(x)=Asin(kx) 0<x<a; Bexp(-qx) x>0
where k=√(2m(E+V0)/ħ and q=√(2m|E|)/ħ
By demanding continuity at x=a for both wave functions and their derivatives I obtained the following solution:
q=-kctg(ka)
How may I proceed? I'd appreciate some guidance.
[/B]