Solutions to Modern Physics II: Quantum Mechanics Homework Set 7 for PHY 373, Assignments of Physics

Download Solutions to Modern Physics II: Quantum Mechanics Homework Set 7 for PHY 373 and more Assignments Physics in PDF only on Docsity! PHY 373 Modern Physics II: Quantum Mechanics, Homework Set 7 Solutions Matthias Ihl 11/09/2007 Note: I will post updated versions of the homework solutions on my home- page: http://zippy.ph.utexas.edu/~msihl/teaching.html 1 Problem 1 For the angular part, we have P = ∫ |Y21(θ, φ)| 2 sin θdθdφ. With Y21 = − √ 15 8π sin θ cos θeiφ, the relevant expression is p(θ, φ) = dP dθdφ = 15 8π sin3θcos2θ. (1) (a) For the first case we get p(π/4, 0) p(π/8, 0) ≈ 3.7 (2) So it’s almost four times more likely to find the electron at θ = π/4. (b) Since p(π/2, 0) = 0, it cannot be found there. 2 Problem 2 The expectation value of r in the groundstate ψ = 1√ πa3 e−r/a is 〈r〉 = 4π πa3 ∫ ∞ 0 r3e−2r/adr = 3 2 a. (3) 1