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HWPhys623_set5 - Homework#5 PHYS 623 Spring 2011 Due...

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Homework #5 — PHYS 623 — Spring 2011 Due Wednesday, Mar-9-2011 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” Time-dependent perturbation theory. Berry phase 1. A charged one-dimensional harmonic oscillator, ˆ H = ¯ ˆ a ˆ a + 1 / 2 , is subjected to a time-dependent electric field, E ( t ). Assuming that the oscillator was in the n -th quantum state at the distant past, t → -∞ , find the transition probability into the k -th state in first order perturbation theory in the distant future, t + . Consider
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