22.6 Sample Test Problems
- Assume an electron is bound to a heavy positive particle with a harmonic potentialV(x) =
1
2 mω
(^2) x (^2). Calculate the energy shifts to all the energy eigenstates in an electric fieldE(in the
xdirection).
- Find the energies of then= 2 hydrogen states in a strong uniform electric field in the z-
direction. (Note, since spin plays no role here there are just 4 degenerate states. Ignore the
fine structure corrections to the energy since the E-field is strong. Remember to use the fact
that [Lz,z] = 0. If you are pressed for time, don’t bother to evaluate the radial integrals.) - An electron is in a three dimensional harmonic oscillator potentialV(r) =^12 mω^2 r^2. A small
electric field, of strengthEz, is applied in thezdirection. Calculate the lowest order nonzero
correction to the ground state energy. - Hydrogen atoms in then= 2 state are put in a strong Electric field. Assume that the 2s and
2p states of Hydrogen are degenerate and spin is not important. Under these assumptions,
there are 4 states: the 2s and three 2p states. Calculate the shifts in energy due to the E-field
and give the states that have those energies. Please work out theproblem in principle before
attempting any integrals.