Why Does an Infinite Potential Barrier Affect Particle Wavefunctions?

[nolanp2]

Homework Statement

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

Homework Equations

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 can't understand why the infinite barrier should have this effect, if it weren't 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?

 

[malawi_glenn]

put up the transmission coefficient 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.