1. The problem statement, all variables and given/known data 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 2. Relevant equations Partition-Function= E= -δ/δβ ln[Z(β)] 3. 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.