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Bound states.

  • #1
880
0

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]
 

Answers and Replies

  • #2
34,056
9,918
How do you get the number of solutions from your last equation?
The borders for "a" and "m" are exactly the limiting cases for 1 and 2 solutions.
 

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