# Qal QuantP1S

Solution:

In our case, using separation of variables, we will get 3 differential equations for x, y and z. W(x,y,z)=w(x)w(y)w(z)

(1)
The same will be for y and z.

Solution of equation (1) is following

• Applying B. C. at x=y=z=0 wave function should be zero, that means B=D=F=0. We have

Also, w(a)=0 which gives . For y component and for z

A, C and E are normalization constants

, limits are from 0 to a.

The eigenfunction for each component will be

The eigenenergies

, ,
Total energy is sum of these energies.

• , where , n=1,2,3...

2.)Solution:

a.)

Dr. Forest: We have not had Perturbation Theory.