A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

302 SOLUTIONS

5.50 Hydrogen in Capacitor (Maryland, Michigan

State)

For time-dependent perturbations a general wave function is

where the satisfy

For the time-dependent perturbation

From Schrödinger’s equation we can derive an equation for the time devel-

opment of the amplitudes

If the system is initially in the ground state, we have and the

other values of are zero. For small perturbations it is sufficient to

solve the equation for

The general probability that a transition is made to state is given by

This probability is dimensionless. It should be less than unity for this
theory to be valid.