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FormulaSheetExam1

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

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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 ω . 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 t 2m x ∂ Ψ ∂ Ψ = + Ψ = = (x) The standard deviation ( ) ( ) 2 2 2 2 x x x x σ = = = x The momentum operator is ˆp i x = = Fourier Transform formulae (Plancherel's Theorem) : 1 2 1 2 f (x) dk F(k)exp(ik x) F(k) dx f (x)exp( ik x) π π = = A useful form of the delta function: 1 2 (x) exp(ik x)dk π δ = The probability current: ( ) * * * i 1 ˆ J(x,t) Im Re p 2m x x m x m ∂ Ψ ∂ Ψ ∂ Ψ Ψ − Ψ = Ψ = Ψ Ψ = = *

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