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## Homework Statement

A particle is in the following potential:

V(x)=infinity for x<0; -V

_{0}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 V

_{0}in terms of the width

*a*and the particle's mass

*m*.[/B]

## Homework Equations

## The Attempt at a Solution

For -V

_{0}<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+V

_{0})/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]