Thermodynamics, Statistical Physics, and Quantum Mechanics

The only change from the harmonic oscillator for a single spring is that,

with two identical springs, the effective spring constant is 2 K.

b) The eigenfunction of the ground state is

c) When one spring is cut, the particle is now coupled to only a single

spring. So we must replace 2K in the above equations by K. The ground

state eigenfunction is now

Notice that The amplitude I for remaining in the ground state

is found, in the sudden approximation, by taking the overlap integral of the

two ground state wave functions. The probability of remaining in the

ground state is the square of this overlap integral:

where we have used in deriving the last line. The probability

of remaining in the ground state is close to unity.

Angular Momentum and Spin

5.22 Given Another Eigenfunction (Stony Brook)

a) The factor cos indicates that it is a state which has an angular
momentum of 1.

266 SOLUTIONS