Lecture8.pptx

# Lecture8.pptx - 1/26/11 RecapofChapter1:TheWaveFuncFon

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1/26/11 1 PHYS 360 Quantum Mechanics Fri Jan 28, 2011 Lecture 8: The Time‐ Independent Schrödinger Equafon HW Assignment 3, due Monday Feb 7: Chapter 2, #4, 5, 7, & 8. Recap o± Chapter 1: The Wave Funcfon i ∂Ψ ( x , t ) t = – 2 2 m 2 Ψ ( x , t ) x 2 + V ( x , t ) Ψ ( x , t ) Ψ ( x , t ) 2 dx = { } a b Probability o± ²nding the parfcle between a and b , at fme t . The fme‐dependent Schrödinger Equafon governs the dynamics o± parfcles in a potenfal V(x,t): What is the meaning o± a parfcle’s wave ±uncfon? Ψ ( x , t ) 2 dx = { } a b Probability o± ²nding the parfcle between a and b , at fme t . Measurement leads to “collapse” o± the wave ±uncfon. f ( x ) = f ( x ) −∞ + ψ *( x ) ( x ) dx σ 2 Δ j ) 2 = ...... = j 2 j 2 = variance = j 2 j 2 = the standard deviation The “expectafon value” is de²ned as: The “spread” (or “uncertainty”) in an expectafon value is given by the standard deviafon: What i± you solve the Schrödinger equafon and come up with some ±uncfon y(x,t) such that y * ( x , t ) y ( x , t ) dx = B 2 −∞ +

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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.

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Lecture8.pptx - 1/26/11 RecapofChapter1:TheWaveFuncFon

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