Calculating Hamiltonian for H-Atom & Energy Changes in Magnetic Field

[hdsncts]

Homework Statement

Write down the full Hamiltonian for a hydrogen atom in an external field. Next, calculate the energy changes deltaE (not absolute E) of the three orbitals Y⁰₁, Y¹₁, and Y^-1₁ induced by the applied magnetic field Bz. Interpret your results with respect to your knowledge of the time-evolution of the wavefunctions.

Homework Equations

The Attempt at a Solution

In all honesty I have no idea how to start this. I know what a Hamiltonian operator is but that's about it. I understand that this forum isn't so that other people can do my homework for me, so can someone help me start in the right direction? Any help would be greatly appreciated.

 

[muppet]

If you know what a Hamilitonian is, you'll know that half of it is the same for everything, and the other half is dependent on the environment. Which is which, and which half is dependent on the environment?

Also, can I clear up how your notation for orbitals works? Looks like it might be different from the one used in my course last year.