Quiz7 - p q B p q p q n n----=- = = + + = (3) Of course, if...

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PHY4221 Quantum Mechanics I (Fall 2004) Quiz 7 (Answers) The normalization gives: ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 ( 29 [ ] { } [ ] { } 2 2 2 0 2 2 0 1 2 2 1 1 2 2 1 1 2 1 0 2 2 2 2 0 1 2 2 1 0 2 2 1 2 sin sin 2 sin sin 2 cos 1 cos 2 1 cos 2 1 1 2 1 2 1 1 2 2 1 2 2 1 / 2 4 2 1, l l l l l l l l l l l l l l d N d N d N d N dx x x N dx x x N d x x x N dy y y y x N dt t t t y N B l l π ψ θ - - - + = = = = - - = - = + - = - - - - - = - = - = - = = + + @ ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 1 1 1 4 2 2 2 ! ! 4 2 2 1 ! l l l l N l l l N l Γ + Γ + = Γ + = + (1) So we have: ( 29 ( 29 2 2 2 1 ! ! ! 1 1 4 2 2 1 ! 2 ! 4 l l l l l N N l l + = = + (2) In the above I used the famous B and Gamma Functions: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 0 1 0 , 1 , 1 ! q p t x B p q dt t t x dte t
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Unformatted text preview: p q B p q p q n n----=- = = + + = (3) Of course, if you did it by integrating by part, that is OK. I am not good at integrals, so I used this or that kind of tricks....
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