sol3.pdf - Graduate QM(PHYS 519 Problem Set#3 Due Friday...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Graduate QM (PHYS 519) Problem Set #3 Due Friday. April 14 1. Impulse in Quantum Mechanics A system experiences a perturbation of the form V = ( t ), where W is a Hermitian operator, so the total Hamiltonian H is given by H = H 0 + V . We have H 0 | k i = E k | k i . Suppose that at t < 0 the system was in the n th state of the discrete spectrum. (a) Determine the probabilities for state k 6 = n for t > 0. This requires using a method other than TD FOPT to determine the time evolution operator U ( t ). (b) For small perturbations V , compare your result to the one obtained using TD FOPT. (c) Suppose W = - Px , where P is a constant parameter with dimensions of momen- tum. Find the resulting U ( t ) and relate the result to the title of the problem. 2. Sudden Approximation A particle moving in one dimension ( x ) is in the ground state of an infinitely deep potential well of width a (0 < x < a ).At t = 0 the right wall of the potential moves in a short period of time τ to the point b > a . Find the
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern