MomentumHermitian

MomentumHermitian - The Momentum Operator is Hermitian...

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Colby College The Momentum Operator is Hermitian Hermitian: Ψ * j o ^ Ψ i dx = Ψ i (o ^ Ψ j ) * dx = Ψ i o ^ * Ψ * j dx p ^ = – ih - d dx Show: - Ψ * j – ih - d dx Ψ i dx = - Ψ i – ih - d dx * Ψ * j dx d Ψ i dx dx = d Ψ i - Ψ * j – ih - d dx Ψ i dx = – ih - - Ψ * j d Ψ i Integration by parts: u dv = uv – v du with u = Ψ * j and dv = d Ψ i – ih - - Ψ * j d Ψ i = – ih - [ Ψ * j Ψ i | x = x = -
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This document was uploaded on 02/22/2012.

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