Homework 7#
This homework is due on Tuesday February 27th. You should submit a PDF of your solutions on myCourses. [Note that we’ll have a break from homework until after reading week so you can get ready for the midterm. Homework 8 will come out on March 12 and will be due on March 19].
Do Townsend 11.1 on the anharmonic oscillator.
An infinite square well between \(x=-a\) and \(x=a\) is perturbed by a potential \(V_1(x) = \lambda x/a\), where \(\lambda\ll 1\). Show that to first order in \(\lambda\), (a) the energy levels are unchanged, whereas (b) the ground state wavefunction is changed. Derive an expression for the ground state wavefunction \(\psi(x)\) that includes the first order correction, evaluating all necessary integrals. Make a plot of \(\psi(x)\) and compare with the original ground state wavefunction, explaining whether the difference makes sense physically.
Do Townsend 11.16 on evaluating \(\langle 1/r \rangle\) for the hydrogen atom.