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HW6 - (a proof(using induction that a a n = n a n-1 n = 1 2...

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PHYSICS 460 Problem Set 6 Due in class Thursday, October 6, 2011 Read all of Chapter 2.6 in Griffiths. 1. Griffiths 2.42 (5 points) 2. Griffiths 2.18 (5 points) 3. Griffiths 2.21 (5 points) 4. Griffiths 2.22 (10 points) 5. (10 points) Using the properties of the raising and lowering operators for the 1- dimensional simple harmonic oscillator
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Unformatted text preview: (a) proof (using induction) that [ a-, ( a + ) n ] = n ( a + ) n-1 n = 1 , 2 , 3 ,... (b) compute Z + ∞-∞ ψ m ( x )( a-) l ψ n ( x ) dx with ψ n ( x ) = ψ * n ( x ) a + a-ψ n ( x ) = nψ n ( x ) R + ∞-∞ ψ m ( x ) ψ n ( x ) dx = δ mn...
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