HWPhys623_set4 - Homework#4 PHYS 623 Spring 2011 Due Monday...

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Homework #4 — PHYS 623 — Spring 2011 Due Monday, FEB-28-2011 at 10:00 a.m. in class Professor Victor Galitski Office: 2330 Physics Class web-page: http://terpconnect.umd.edu/ galitski/PHYS623/ . Write clearly your name and the homework number and staple the pages together. Teaching Assistants: Meng Cheng; Office: PHS2113, Tel: 301.405.7299 , Email: [email protected] Joe Mitchell; Office: PHS3117, Tel: 405.301.2659, Email: [email protected] Textbooks: J. J. Sakurai and J. J. Napolitano, “Modern Quantum Mechanics” L. D. Landau and L. M. Lifshitz, Vol. III: “Quantum Mechanics Non-Relativistic Theory” Sudden perturbations. Transition probabilities. 1. Fifty thousand Rubidium-87 atoms are confined in a three-dimensional harmonic trap and cooled down to near-absolute zero temperature. The trap frequency is initially ω T = 2 π × 30 Hz, but then, at t = 0, it changes suddenly to ˜ ω T = 2 π × 15 Hz. Assume that all atoms are initially in the ground state and (a) Calculate (approximately) the number of atoms that will be excited by the sudden perturbation ( i.e. , the number of atoms propagated to any excited state in the new harmonic potential). (b) Difficult problem (optional): Estimate the temperature, T f , that the system will have at t → ∞ , when relaxation processes will bring it to equilibrium.
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