Problem Set 9 for PHY4605: Introduction to Quantum Mechanics II - Spring 2005, Assignments of Physics

Download Problem Set 9 for PHY4605: Introduction to Quantum Mechanics II - Spring 2005 and more Assignments Physics in PDF only on Docsity! PHY4605–Introduction to Quantum Mechanics II Spring 2005 Problem Set 9 March 30, 2005 Due: April 6, 2005 Reading: Griffiths Ch. 11 1. Well . Consider a spherically symmetric flat potential well, V (r) { −V0 r ≤ r0 0 r > r0 where V0 and r0 are positive real constants. (a) Find the differential scattering cross section for this potential in Born approximation and in the limit of low energy, E = h̄2k2/2m, such that kr0 ¿ 1. (b) Find the s-wave phase shift δ0 produced by this potential. To simplify the calculation, consider the low energy limit, and assume the scattering potential is weak, so that (mV0) 1/2r0 ¿ h̄. (1) The first step is to find the solution to the one-dimensional Schrödinger equation for the s-wave radial wave function at r < r0 with the right boundary condition at r = 0. The matching condition at r = r0 gives an equation for the phase shift, δ0. (c) Find the low energy scattering cross section from the phase shift found in part b). The result should agree with what you found in part a)! 2. Griffiths Problem 11-8. 3. Griffiths Problem 11-9. 1