# Quantum oscillator statistics

1. Nov 3, 2013

### aaaa202

Just one short question about something I didn't understand in my book: "At low temperaturs only vibration modes where hω<kT will be excited to any appreciable extent. The excitation of these modes will be approimately classical each with an energy close to kT."
I don't understand the last sentence. What is meant by a classical exciation? The energy of the modes will be (n+½)hω for which there is a probability distribution - on this ground how can you say that the energy of each excitation is approx kT?

2. Nov 3, 2013

### DrDu

What is meant that $\langle E \rangle_T-\langle E \rangle_0\approx kT$