Compute the partition function of a quantum harmonic oscillator with frequency w and energy levels Ex....

 

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Compute the partition function of a quantum harmonic oscillator with frequency w and energy levels Ex. - Now (n + ²) En hw = Find the average energy E and entropy S as a function of temperature T Einstein constructed a simple model of a solid as N atoms, each of which vibrates with the same frequency w. Treating these vibrations as a harmonic oscillator, show that at high temperatures, kBT » ħw, the Einstein model correctly predicts the Dulong-Petit law for the heat capacity of a solid ne Z Cv=3NkB At low temperatures, the heat capacity of many solids is experimentally observed to tend to zero as Cy~ T³. Was Einstein right about this? Compute the partition function of a quantum harmonic oscillator with frequency w and energy levels Ex. - Now (n + ²) En hw = Find the average energy E and entropy S as a function of temperature T Einstein constructed a simple model of a solid as N atoms, each of which vibrates with the same frequency w. Treating these vibrations as a harmonic oscillator, show that at high temperatures, kBT » ħw, the Einstein model correctly predicts the Dulong-Petit law for the heat capacity of a solid ne Z Cv=3NkB At low temperatures, the heat capacity of many solids is experimentally observed to tend to zero as Cy~ T³. Was Einstein right about this?