HW10 - PHYSICS 4455 QUANTUM MECHANICS Problem Set 10 due...

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PHYSICS 4455 — QUANTUM MECHANICS Problem Set 10 — due 12 / 2 / 2005, 5pm in D)r. Schmittmann’s office. 1. Angular momentum and its commutators – part of every physicist’s rate of passage! Confirm Liboff Eq. (9.8) and (9.13). Do Liboff Problems 9.4 (takes just a few minutes), 9.7 (all of it!) and 9.11 (only parts a and c). Show every step explicitly. 2. The isotropic harmonic oscillator in two dimensions. A non-relativistic, structureless particle of mass M is confined by a harmonic oscillator potential of the form V ( x , y )= 1 2 M ω 2 ( x 2 + y 2 ) The following sequence of steps takes you through the solution of the associated, two-dimensional Schrödinger equation. The notation follows the class notes. (i) Write down the stationary Schrödinger equation for this problem, using two-dimensional polar coordinates ρ and φ . Show that Ĥ , L z = 0 and reduce the eigenvalue problem to the radial differential equation for R m (ρ) . (ii) Examine this differential equation in the limit of
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HW10 - PHYSICS 4455 QUANTUM MECHANICS Problem Set 10 due...

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