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?
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).