Rigid Rotator Model: Exploring O2's Magnetic Moment

[skrtic]

Homework Statement

A diatomic molecule such as O2, can be thought of as a rigid rotator (dumbbell molecule) if its energy is not too large. Assume that the rotator consists of two identical masses, M, separated by a constant distance, R. (a) Find the energy eigenvalues and eigenkets of the rigid rotator. Now assume that the masses have a charge, Q. (b) Find the magnetic moment corresponding to the energy eigenvalues. Now imagine that a magnetic field, B, defines the z-axis. (c) Find the “allowed” z-components of the magnetic moment. (d) Find the angles that the magnetic moment vector makes with the z-axis.

Homework Equations

Not really sure.

The Attempt at a Solution

Alot of my problem is that I've been self teaching myself quantum mechanics by reading the book (Shankar) and it really has not been working for me in terms of concepts and grouping concepts.

When i read the problem i initially think of finding the Hamiltonian of the system, but that does not seem to fit into the chapter or section, and i still get very confused with eigenstates and eigenvalues when applied to something that is not a matrix (I understood how do get them in terms of linear algebra with numbers in a matrix, but the eigenvalue of an energy at this point has no meaning to me.)

Any guidance would be great. Sorry i can't supply more information but this problem really has stopped me dead in my tracks.

 

[BigJDubs]

I think it would be helpful if someone can explain the concepts and how to apply them to the problem. Thanks!