We have taken the energy of a simple harmonic oscillator. because we are assuming the atoms are vibrating within a simple harmonic potential. (a) is it justified to take the potential of an simple harmonic oscillator? hint: use taylor series expansion of potential as function of position around minimum] (b) is the potential of simple harmonic oscillator still valid at high tem- perature? determine the higher order correction of potentia (c) is the thermal expansion of solids possible, just taking care of the har monic potential? justify your answer using calculation (d) take correction of potential upto fourth order in displacement and calculate the average displacement of the atoms as a function of tem- perature