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

258 SOLUTIONS

where we used the fact that The probability of energy

So the probability of is given by

where

It is easy to show that this quantity is less than unity for any value of

and is unity if

5.15 Harmonic Oscillator ABCs (Stony Brook)

a) Here we took

since the commutator

b)

c)

and finally