10pt Consider the same 1D harmonic oscillator in Problem 1. Let Nbe the number operator and cdots be the thermalaverage ofan operator Aat thermal equilibrium with temperature T=1kB. Prove that[N2]=2e-2Z[H]where His the Hamiltonian and Z=Tr[e-H]is the partition function. If you want, you may use the following relations.n=0e-an=ea22csch(a2)n=0ne-an=14csch2(a2)n=0n2e-an=14csch3(a2)cosh(a2)