From this expression, it is easy to see that for large values of β β , for very low temperatures, the average energy U in the Harmonic oscillator approaches zero very quickly, exponentially fast. The reason is that kT is the typical energy of random motion at temperature T, and when this is smaller than ℏ ℏ ω ω , there is not enough energy to give the oscillator even one quantum of energy. So the oscillator stays in its ground state, storing next to no energy at all.