Practice Test 1 - Introduction to Quantum Mechanics - Fall 2004 | PHY 4604, Exams of Physics

Download Practice Test 1 - Introduction to Quantum Mechanics - Fall 2004 | PHY 4604 and more Exams Physics in PDF only on Docsity! PHY4604–Introduction to Quantum Mechanics Fall 2004 Practice Test 1 October 4, 2004 These problems are similar but not identical to the actual test. One or two parts will actually show up. 1. Short answer. • Explain the photoelectric effect • Explain the significance of h̄ in quantum mechanics, and give an example of a place where it shows up. • Discuss the uncertainty principle briefly • Explain the difference between the 2 versions of Schrödinger’s equation ih̄ ∂ψ ∂t = − h̄ 2 2m ∂2ψ ∂x2 + V ψ and − h̄ 2 2m ∂2ψ ∂x2 + V ψ = Eψ • What are the units of P (x, t), the probability density in 1 dimension? Justify your answer. • Calculate the commutator [px, x2] • Calculate the expression for the Bohr levels of the hydrogen atom from the Bohr-Ehrenfest quantization condition. 2. Consider a wave packet defined by ψ(x) = ∫ ∞ −∞ dkf(k)ei(kx−ωt) (1) with ω = h̄k2/2m and f(k) given by f(k) =    0 k < −∆k/2 a −∆k/2 < k < ∆k/2 0 ∆k/2 < k (2) (a) Find the form of ψ(x) at t = 0. 1