Problem 2.Energy of the quantum harmonic oscillatorRecall from Homework 5 Problem 1 that the mean energy of a single classical harmonicoscillator interacting with the thermal environment is(E) = k„T(13)Now we will compare this classical result to the quantum version of the harmonic oscillator.This builds on Homework 4 Problem 3 and Homework 5 problem 3.Recall that the energy levels of the oscillator are E, = nhun, where we have shifted whatwe call zero energy to be ground state energy n =%3D0. while higher vibrational states haven= 1,2.....(a) Determine the average energy (E) of the quantum harmonic oscillator at temperatureT or 3 = 1/k T, using the partition function. Express your result using B and hun.You can check your result using the next item.%3!(b) How is the mean vibrational quantum number (n) related to (E)? Plot the meannumber of vibrational quanta (n) versus kT/hn for kT/ha(from your graph) the temperature in units of hg where (n) = 1.= 0...4. Determine%3D(c) Plot(E)(14)versus k„T/hwo for kaT/h=0...4.

a) Given for an Quantum Harmonic oscillator,En=nkω where n=0,1,2,...the partition function is…

Answered: (a) Determine the average energy (E) of…

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