Lecture6.pptx - 1/24/11 PHYS360QuantumMechanics...

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1/24/11 1 PHYS 360 Quantum Mechanics Mon Jan 24, 2011 Lecture 6: If we make momentum an operator , will it agree with classical physics? Homework Set 2: Ch 1 ‐# 8, 9, 15, 17 IMPORTANT: Room change – move next door to Rm 331 Starts Wednesday. x = x Ψ x , t ( ) 2 dx −∞ + For par[cle in a given state, the expecta[on value for its posi[on is: Reminder: the expecta[on value is the average of repeated measurements on an ensemble of iden[cally prepared systems. How does <x> change with [me? Will this look like the velocity? d x dt = x t Ψ 2 dx = i 2 m x x Ψ * ∂Ψ x ∂Ψ * x Ψ dx We’ve used the results of last lecture’s deriva[on that the normaliza[on is constant. Should x be a func[on of [me? Integration by parts: f dg dx dx = df dx g dx + fg a b a b a b d x dt = x t Ψ 2 dx = i 2 m x x Ψ * ∂Ψ x ∂Ψ * x Ψ dx d x dt = i m Ψ * ∂Ψ x dx d x dt = i 2 m Ψ * ∂Ψ x ∂Ψ * x Ψ dx Now, integrate by parts again, but just on the second term: We will postulate
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This note was uploaded on 04/23/2011 for the course PHYS 360 taught by Professor Durbin,stephen during the Spring '11 term at Purdue University-West Lafayette.

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Lecture6.pptx - 1/24/11 PHYS360QuantumMechanics...

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