Quantum Mechanics - Problem Set 3 with Solutions | PHY 215C, Assignments of Quantum Mechanics

Download Quantum Mechanics - Problem Set 3 with Solutions | PHY 215C and more Assignments Quantum Mechanics in PDF only on Docsity! PROBLEM SET 3 Physics 215C- Quantum Mechanics, SPRING 2008 (Due Wednesday, April 30.) 1. (Shankar Exercise 19.3.2) Show that if V (r) = −V0 θ(r0 − r), dσ dΩ = 4r20 ( µV0r 2 0 h̄2 )2 (sin qr0 − qr0 cos qr0) 2 (qr0)6 . Show that as kr0 → ∞ the scattering becomes isotropic and, σ ≈ 16πr20 9 ( µV0r 2 0 h̄2 )2. (Here and in problem 2, recall that for elastic scattering the magnitude of the incoming and outgoing momenta k is related to the magnitude of the momentum exchanged q by q2 = 2k2(1 − cos θ). 2. (Shankar 19.3.3) Show that for the Gaussian potential, V (r) = V0 e −r2/r2 0 , dσ dΩ = πr20 4 ( µV0r 2 0 h̄2 )2 e−q 2r2/2 σ = π2 2k2 ( µV0r 2 0 h̄2 )2 (1 − e−2k 2r2 0). Hint: Since q2 = 2k2(1 − cos θ), we have d(cos θ = −d(q2)/2k2.)