A small system has two normal modes of vibration, with natural frequencies ω1 and ω2=2ω1. What is the probability that, at temperature T, the system has an energy less than 5ω1/2? The zero of energy is taken as its value at T=0.
Answer:
(1+x)(1+x2)(1+x+2x2)where x≡exp(−βℏω1)