[Hunt]

Why is it that when considering a particle moving in 1D , the potential energy V of this particle tends towards infinity at the bounderies of the wall ? What is the physical reason ? Is this a consequence of the SE equation as Psi must be 0 at the boundaries / outside the box , then V=infinity satisfies just that ? 

[Yggdrasil]

It greatly simplifies the analysis because an inifinite potential outside the box ensures that your wavefunction is zero anywhere outside the box.  If you solve the particle in a box using a finite potential outside of the box, you see tunneling occur, that is you have a small probablility that your particle lies outside of the box.

So in short, an inifinite potential outside of the box ensures a zero probability of being outside of the box.  The boundary conditions (that the wavefunction is zero at the edges of the box) are a consequence of this potential.

[Hunt]

Thanks Yggdrasil .It makes a bit more sense now.