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obi-wan

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## Homework Statement

A quantum mechanical harmonic oscillator with resonance frequency

**is placed in an environment at temperature**

*ω***. Its mean excitation energy (above the ground state energy) is 0.3ħω.**

*T*Determine the temperature of this system in units of its Einstein-temperature ΘE = ħω/kB

## Homework Equations

Partition-Function= E= -δ/δβ ln[Z(β)]

## The Attempt at a Solution

I have used the Partiton-Function, E= -δ/δβ ln[Z(β)] = -δ/δβ ln[(x^1/2)/1-x]

.where x= exp^(ħω/2)

E= -[δ/δβ ln(exp^-ħωβ / 1-exp^-ħωβ] = Eo - exp^-ħωβ / -1 + exp^-ħωβ

. where Eo= ħω/2

E= Eo + εħω

.where ε = 0.3ħω

I need find β in order to work out the temperatureof the system but stuck at this point. Really appreciate if some one can guide me in the right direction.