Lecture_06

Lecture_06 - PHYS 342 Fall 2010 Lecture Lecture 06: Solving...

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HYS 342 PHYS 342 Fall 2010 ecture 06: olving the Schrödinger Wave Lecture 06: Solving the Schrödinger Wave Equation in one dimension Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 06
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Important Results…so far 22 2 () 2 iU x tm x   Time-dependent Schrödinger Wave Equation in one dimension – stationary states When U(x), are independent of time, we have 2 2 Ux E mx     Time-independent Schrödinger Wave Equation in one dimension For example, when applied 2 to the hydrogen atom : 1 4 o e U x U r r   The calculated values of E exactly match Bohr’s results from 1911!
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) kx t Picturing the time-dependent wave function What is Ψ (x=x t=0)? x () 2 ; 2 x ikx t Ae k f    What s ( o t) ? x The picture at some particular value of =x hen t=0 Imag. A Imag. x x o when t 0 λ eal iAsin k x x o k x x o Real A x=x o Real Acos k x x o s t increases the x=0 As t increases, the helical spring rotates CCW at ω t
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x=0 x=x o Defining positive rotation (CW ) What’s with the - ω t? X x 360 o rotation thru otion in - X + ω t (CW) Motion in x X 360 o rotation thru (CCW) Motion in +x ω t (CCW)
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What is physical interpretation of Ψ ?
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Lecture_06 - PHYS 342 Fall 2010 Lecture Lecture 06: Solving...

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