Thermodynamics, Statistical Physics, and Quantum Mechanics

QUANTUM MECHANICS 303

a) For the state the probability is zero. It vanishes because the

matrix element of is zero: because of parity. Both S-

states have even parity, and has odd parity.

b) For the state the transition is allowed to the
orbital state, which is called The matrix element is similar to the
earlier problem for the Stark effect. The 2P eigenstate for , is
in (S.5.48.5) and that for the 1S state is exp The integral
is

where is the Bohr radius of the hydrogen atom.

5.51 Harmonic Oscillator in Field (Maryland,

Michigan State)

We adopt (S.5.50.4) and (S.5.50.5) for the time-dependent perturbation
theory. Now we label the eigenstates with the index for the harmonic
oscillator state of energy and write the equation satisfied
by the time-dependent amplitudes

We need to evaluate the matrix element of between the states
and of the harmonicoscillator. It is onlynonzero if In
terms of raising and lowering operators,