Lecture8 - RecapofChapter1:TheWaveFuncFon FriJan28,2011...

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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 of 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 of finding the parFcle between a and b , at Fme t . The Fme‐dependent Schrödinger EquaFon governs the dynamics of parFcles in a potenFal V(x,t): What is the meaning of a parFcle’s wave funcFon? Ψ ( x , t ) 2 dx = { } a b Probability of finding the parFcle between a and b , at Fme t . Measurement leads to “collapse” of the wave funcFon. f ( x ) = f ( x ) −∞ + ψ *( x ) ψ ( x ) dx σ 2 ( Δ j ) 2 = ...... = j 2 j 2 = variance σ = j 2 j 2 = the standard deviation The “expectaFon value” is defined as: The “spread” (or “uncertainty”) in an expectaFon value is given by the standard deviaFon: What if you solve the Schrödinger equaFon and come up with some funcFon y(x,t) such that y * ( x , t ) y ( x , t ) dx = B 2 −∞ +
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