Effects of Magnetic field applied to Hydrogen-like atom.

cwatson · Apr 21, 2009

1. Apply a magnetic field B to a hydrogen like atom. This gives rise to an additional potential energy term of mu_b*B*L_z/hbar

a) Show that the eigenfunction PSI_nlm is still an eigenfunction in the presence of the magnetic field

b) Show that the eigenvalues are E_n + m*mu_b*B

How do you show that the eigenfunction remains?

Matterwave · Apr 22, 2009

What's the usual Eigenfunction equation? (Hint, it is Schroedinger's equation), how has that changed with this added potential energy term?

Alternatively, does this new Hamiltonian commute with the old one? What do commuting operators have in common?

Effects of Magnetic field applied to Hydrogen-like atom.

1. How does a magnetic field affect the energy levels of a hydrogen-like atom?

2. What is the significance of the Paschen-Back effect in the study of hydrogen-like atoms in a magnetic field?

3. How does the orientation of a magnetic field affect the energy levels of a hydrogen-like atom?

4. What is the role of the spin of an electron in the behavior of a hydrogen-like atom in a magnetic field?

5. How do the principles of quantum mechanics help explain the effects of a magnetic field on a hydrogen-like atom?

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