Homework Set 6 - Quantum Mechanics II | PHYS 5260, Assignments of Quantum Mechanics

Download Homework Set 6 - Quantum Mechanics II | PHYS 5260 and more Assignments Quantum Mechanics in PDF only on Docsity! Leo Radzihovsky, Spring 2008 PHYS 5260: Quantum Mechanics - II Homework Set 6 Issued April 11, 2008 Due April 28, 2008 Reading Assignment: Shankar, Ch.20 1. Derive particle continuity equation for the Dirac equation, identifying the relativistic particle number and current densities in terms of the Lorentz spinor, ~ψ. 2. Starting with the 3d Dirac equation in a magnetic field, B derive the corresponding nonrelativistic Schrodinger, i.e., the Pauli equation, showing how the spin emerges and gives Zeeman interaction with the B field (in addition to the orbital effect of the field). Identify the g factor (showing that g = 2) and the relation between the electron’s magnetic moment and its spin S. 3. Using your solution to the above problem and your knowledge of the spectrum (from previous homeworks) for a nonrelativistic particle in a constant magnetic field, find the exact spectrum of a relativistic electron in a constant B-field. Hint: for the interpretation of the negative energy solutions, see the end of Ch.20.