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## Homework Statement

I must find the average number of energy levels of quantum harmonic oscillator at temperature T, and the answer is given as

I must use Boltzmann distribution and the sum of geometric progression. For finding the average value I must use the equation

<F>=trace(F*rho)

Where rho is the density matrix, given as

Where p is the probability and n is the energy eigenstate of oscillator. For F I must use b

^{+}b

## Homework Equations

## The Attempt at a Solution

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