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obi-wan
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Homework Statement
A quantum mechanical harmonic oscillator with resonance frequency ω is placed in an environment at temperature T. Its mean excitation energy (above the ground state energy) is 0.3ħω.
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.