Application of Schrodinger wave equation: Electron in an infinitely deep potential well (one dimension):

Consider an electron placed in an infinitely deep potential well with width 'a'. It is assumed that the movement of the electron is restricted by the walls and the electron is moving only in the   x-direction. The collision of electrons with walls is perfectly elastic. Since the electron is moving freely, inside the well its potential energy V = 0 and V =  outside the well so electron cannot escape from the well through the sides.