# Infinite potential barrier

1. Jan 24, 2008

### nolanp2

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

find the wavefunction of a particle in a potential
V(x)= 0, |x|< a
V, |x|< b (V>0)
(Infinity), |x|>=b

ground state energy 0<=E<=V

2. Relevant equations

3. The attempt at a solution
i know the wavefunction has to be equal to zero at the infinite barrier so when i use that as my boundary condition for the V potential region i just get that the particle has zero probability of being in this region at all, leaving only the zero potential region for it to lie within. but i cant understand why the infinite barrier should have this effect, if it werent for this barrier the particle would be able to reach this higher energy region. can any1 help me with an explanation of this effect, or if it is not the case point out where i'm going wrong?

2. Jan 24, 2008

### malawi_glenn

put up the transmission coefficent as a function of the barrier height, and you'll see that it goes to zero as the barrier height goes to zero.

And for the criteria that the wave function must be continous, it must be zero at the boarder and the wave function must be zero in the infinite region, since the particle can penetrate through it.