Quantum Mechanics I HW1: Compton Scattering, Fields, Semiclassical Transitions, Assignments of Quantum Mechanics

Download Quantum Mechanics I HW1: Compton Scattering, Fields, Semiclassical Transitions and more Assignments Quantum Mechanics in PDF only on Docsity! PHY-851 QUANTUM MECHANICS I Homework 1, 30 points September 3 - 10, 2003 Introduction. Reading: Messiah, Chapter 1. 1. /6/ Consider a two-step process. A photon with the wave length 0.02 nm underwent Compton scattering by an angle of 120◦ off an electron at rest. The scattered photon knocked out the deepest bound electron from a molibdenum atom. Evaluate the kinetic energy of the photoelectron emitted at the second step. 2. /10/ For the lowest electron orbit in the hydrogen atom a. estimate magnitude of the electric field of the nucleus at the orbit (in V/cm); b. estimate magnitude of the magnetic field created at the nucleus by the orbital motion of the electron (in Tesla); c. compare the Coulomb and gravitational forces between the electron and the proton. In all cases give the numbers! 3. /6/ Messiah, Problem 6, p. 44. 4. /8/ a. Consider the semiclassical transitions between the levels n and n′ in the Bohr theory of the hydrogen atom, assuming n, n′  1 and ∆n = |n − n′|/n  1. Show that the correspondence principle holds, namely that the quantum radiation frequencies coincide with those predicted for a classical particle with a revolution frequency for the relevant orbits (the last part of Problem 7, Messiah, p. 44). b. Prove that this correspondence is fulfilled for any potential well, where the periodic motion of a particle is quantized in accordance with the Bohr quantization rule, ∮ p dx = 2πnh̄. (1) /Consider the momentum p along the classical orbit as a function of x and energy En, which is a continuous function of n, and take a derivative with respect to n./ 1