Deduce an expression for the root mean square energy, 2 1/2 , in terms of the partition function and hence an expression for

Deduce an expression for the root mean square energy, 〈ε²〉^1/2, in terms of the partition function and hence an expression for the root mean square deviation from the mean, Δε=(〈ε²〉 – 〈ε〉²)^1/2. Evaluate the resulting expression for a harmonic oscillator.