# Harmonic oscillator probability

1. Aug 15, 2006

### octol

Hello all,
if I have an ion trapped in a harmonic oscillator potential with a resonant frequency 0f 11 MHz and the ion cooled to a temperature of T=0.48mK, how do I find the probability that the oscillator is in its ground state?

I know that the ground state energy is $$1/2 \hbar \omega$$, but how do I connect this to the given temperature? And even then, how do I get the probability?

Best regards

2. Aug 17, 2006

### octol

I need help on this one, it is probably an easy problem for a lot of you.

Best regards,
Jon

3. Aug 18, 2006

### Philcorp

Have you taken a course in statistical mechanics before? Id say that the equipartition theorem probably holds the answer to your question.