Spring 2022 Homework Assignments

**Homework 1: (Due Monday, March 7)**Find the change in the energy of an electron in an infinite square well potential, due an applied electric field E. The electric field may be assumed to result in a perturbing potential of the form H

_{1}= e E x. Find the correction to the energy of the n'th state to second order in peerturbation theory, in the form of a series.**Homework 2: (Due Monday, April 11)**Use the variational method to estimate the ground state energy of a quantum particle in the one dimensional potential V(x) = - V

_{o}exp(-(x/x_{o})^{2}) where V_{o}and x_{o}are positive constants with appropriate units. Use your favorite trial wavefunction. Evaluate the numerical factor multiplying the term with the energy units, so that we can compare and see who gets the lowest energy!

Each homework is to be placed as a single PDF document (which may contain photos of your work) and submitted through moodle.

Please name the file in the format:

Also, please make sure you include the submission date on the first page so that we can account for early/late submissions.

Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.