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sum1_ssp - Summary 0 Quantum mechanics Axioms 1 State of a...

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Summary S-1 0. Quantum mechanics Axioms: 1) State of a physical system state function ψ 2) Physical quantity A linear Hermitian operator A 3) State in which A has a sharp value ψ with A ψ = a ψ 4) ψ = c f i i i Contribution of f i to measurable quantities given by contribution to ψ 2 . Average value of quantity A in state ψ : A r r d r r r d r = = ψ ψ ψ ψ ψ ψ ψ A A 2 3 3 * * ( ) ( ) ( ) ( ) Position operator: r ψ ψ = r eigenfunction to eigenvalue r r r 0 0 : ( ) ψ δ
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Summary S-2 Momentum operator: p ψ ψ = − i h eigenfunction to eigenvalue p e e i pr ik r : ψ = plane waves with wave vector k p = / h and de Broglie wave length λ = h p / Probability density: ψ ( ) r 2 Normalization: ψ ( ) r d r V = 2 3 1 probability of presence in V Wave packet: ψ ( ) ( ) x f p e dp ipx = (1-dim), superposition of plane waves Heisenberg principle of uncertainty: ∆ ∆ x p
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