Hey topsquark,

Huge Quantum exam tomorrow! Few practice probs I didn't understand:

1.) Suppose that an atom in a solid is described by

, where

is the hamilotonian, and

. Also

is needed for the vibrations of an atom (in an object).

is a real constant. Determine the

-th energy eigenvalue

of

, assuming

's

-th eigenvalue

is also the

-th[/tex] energy eigenstate of

.

2a.) Using quantum mechanics, describe how you'd solve the system of a hydrogen atom. What are the physical results?

Mr F says: This is most certainly found in any quantum mechanics textbook .....
b.) Use separation of variables in

coordinates in order to solve the time-indep. schrodinger equation for a particle (free) that's restricted to a 2-D square box. The PE (potential) of this system is:

.

c.) Determine all energy eigenfuntions and their energy eigenvalues. Then, determine what the degeneracy of the energy state

. (Note,

is the lowest level).