851_09outline - PHYS851 Quantum Mechanics I, Fall 2009...

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PHYS851 Quantum Mechanics I, Fall 2009 Semester Outline 1. Dirac Notation (a) Bras and Kets i. Hermitian conjugation (b) Operators i. Hermitian conjugation of operators ii. Properties of Hermitian operators iii. Properties of Unitary operators (c) c-numbers i. The inner product ii. Matrix elements (d) Hilbert Spaces i. Discrete indices A. Summation over indices B. Orthonormality via Kronecker delta C. Vector/Matrix and Tensor representations ii. Continuous indices A. Integration over indices B. Orthonormality via Dirac delta C. Single- and multi-variable function representations 2. Quantum Postulates (a) Closed system described by state vector in Hilbert space (b) Observables described by Hermitian operators (c) Evolution of state vector governed by Schr¨odinger’s equation (d) Measurement Postulates i. Possible results of a single measurement ii. Probabilities associated with possible results iii. Wave function ‘collaps’ occurs immediately after result obtained 1
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3. Rabi Model (a) Two-level approximation
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This note was uploaded on 12/21/2011 for the course PHY 851 taught by Professor Moore,m during the Fall '08 term at Michigan State University.

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851_09outline - PHYS851 Quantum Mechanics I, Fall 2009...

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