QM-notes-2011 - School Of Mathematics, Statistics, and...

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Unformatted text preview: School Of Mathematics, Statistics, and Operations Research Te Kura M atai Tatauranga, Rangahau Punaha MATH 321/322/323 Applied Math (Quantum Physics) T1 and T2 2011 Math 322: Applied Mathematics Notes Quantum Physics module Matt Visser School of Mathematics, Statistics, and Operations Research Victoria University of Wellington, New Zealand. E-mail: matt.visser@mcs.vuw.ac.nz URL: http://www.mcs.vuw.ac.nz/visser Version of 23 February 2011; L A T E X-ed February 24, 2011 Warning: These notes will basically be the textbook for this module. This is a reading course, so these notes, and various web resources, should be your primary source of information. I may also assign some specific supplementary reading. There are still a few rough edges in these notes. If you find errors, typos, and/or obscurities, please let me know. Contents 1 Overview 4 2 Introduction to quantum physics 6 2.1 Quantum mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Quantum technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Quantum field theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Classifying the theories of physics: Superb , Useful , and Tentative . . . 8 2.5 Superb means Never to be Discarded . . . . . . . . . . . . . . . . . . . 10 2.6 Textual analysis: A warning . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Filtering out the nonsense . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7.1 The two faces of physical theory . . . . . . . . . . . . . . . . . . . . 12 2.7.2 Rules based on mathematical consistency . . . . . . . . . . . . . . . 13 2.7.3 Parameterized post classical formalism? . . . . . . . . . . . . . . . . 15 2.7.4 High weirdness in quantum field theory . . . . . . . . . . . . . . . . 16 2.7.5 The rough guide to crackpot filtering . . . . . . . . . . . . . . . . . 17 2.8 Last words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Heisenberg uncertainty principle 20 3.1 Fourier transforms and signal theory . . . . . . . . . . . . . . . . . . . . . 20 3.2 The de Broglie and Einstein relations . . . . . . . . . . . . . . . . . . . . . 26 3.3 The Heisenberg uncertainty principle . . . . . . . . . . . . . . . . . . . . . 26 3.4 Classical operators and commutators . . . . . . . . . . . . . . . . . . . . . 28 3.5 Proof of the classical uncertainty relation . . . . . . . . . . . . . . . . . . . 32 3.6 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Tunnelling 35 4.1 Sound penetrating a barrier . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Radio penetrating a barrier . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3 Frustrated total internal reflection . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 Key idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3.2 Reminder: Snells law . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3.34....
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This note was uploaded on 07/14/2011 for the course MATH 322 taught by Professor Matt during the Spring '11 term at Victoria Wellington.

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QM-notes-2011 - School Of Mathematics, Statistics, and...

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