FormulaSheetExam1

FormulaSheetExam1 - Formula Sheet for Exam 1 (These...

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Formula Sheet for Exam 1 (These formulas will be given.) (I will not give the de Broglie relations, or the definitions of the wave number k and the angular frequency ϖ . I expect you to memorize those.) The classical wave equation: 2 2 2 2 2 f (x, t) 1 f (x, t) x v t = The time-independent Schrödinger Equation: 2 2 2 i V(x) t 2m x Ψ Ψ = - + Ψ h h The standard deviation ( 29 ( 29 2 2 2 2 x x x x x σ = = - = - The momentum operator is ˆp i x = h Fourier Transform formulae (Plancherel's Theorem) : 1 2 1 2 f (x) dk F(k)exp(ik x) F(k) dx f (x)exp( i k x) π π = = - A useful form of the delta function: 1 2 (x) exp(ik x)dk π δ = The probability current: ( 29 * * * * i 1 ˆ J(x, t) Im Re p 2m x x m x m Ψ Ψ Ψ Ψ - Ψ = Ψ = Ψ Ψ h h
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Exam 1 Review Topics: Ch 1 and Ch 2 in Griffiths, Homeworks 1 thru 5, and Lecture Notes up thru/including "Dirac Delta function" probability density and the wavefunction normalization of the wavefunction computation of expectation values and standard deviation, given a wavefunction
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.

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FormulaSheetExam1 - Formula Sheet for Exam 1 (These...

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