Q1) Consider a particle in a one-dimensional infinite well with walls at x=0 and x=a.Suppose a perturbation is applied so that the potential energy is shifted by an amount(0)= n²h?/(2ma²) is the ground state energy(0)a H, = 10-3E," (x/a)², where E") ofthe unperturbed box.a) Calculate the first order correction to all excited state energies due to theperturbation.b) Calculate the second order correction to all excited state energies due to the perturbation.(Simplify your result as much as you can, f.eg. taking sin[(k ±n)T] = 0)c) Calculate the first order correction to the wave function due to the perturbation.d) Write down the approximate wave function of the perturbed well for the state withn = 3 corrected up to the 1.st order in perturbation theory . Consider only the firstthree non-zero terms in the sum.

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Answered: Q1) Consider a particle in a…

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