The details of several steps in the particle-in-a-box model in this chapter have been om...

The details of several steps in the particle-in-a-box model in this chapter have been omitted. Work out the details of the following steps:

a. Show that if = A sin rx + B cos sx ( A , B , r , and s are constants) is a solution to the wave equation for the one- imensional box, then

b. Show that if = A sin rx, the boundary conditions ( = 0 when x = 0 and x = a) require that where n = any integer other than zero .

c. Show that if the energy levels of the particle are given by

d. Show that substituting the value of r given in part c into = A sin rx and applying the normalizing requirement gives