05_04_13 - [email protected] 134 Expectation...

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Unformatted text preview: [email protected] 134 Expectation values for p x 04/02/2003 V(x) x 1 x 3 x… x n-1 x 2 x n < < ¡ < ¢ < … < n £ < n ) ( 1 1 ) ( 1 1 t x k i n n t x k i n n n n n n e A e A ϖ ϖ- + +- + + = Ψ = Ψ ) ( ) ( 2 2 1 1 ∆ ∆ + + + Ψ =- Ψ n n n n x x Ψ = Ψ → ∆ Ψ + Ψ ≈ Ψ = Ψ = = Ψ ∂ ∂ ∆ +- +-- + + + + ∆- ∆ + + ∆ + + ∆ k i t x ik e e e e A x n n n i n k k i n t i x k x k x k i n n n k n k n n n n n n n n ) , ( } 2 1 2 1 2 1 1 2 1 1 2 ] [ ] ) ( ) ( [ 1 ϖ 04/13/2005 Review of one dimension: Conclusion: whenever needs to be computed, one can use Ψ- ∂ ∂ x i Ψ k ) ( ) ( 1 2 1 1 2 ∆ + + ∆-- + + = n n n n x ik x ik n n e e A A ( 29 ( 29 ∫ ∑ ∑ ∞ ∞- ∂ ∂ ∂ ∂ Ψ- Ψ = Ψ- Ψ = Ψ = dx i dx x i dx k p x j j x j j j j x ! ! ! * all * all 2 ) ( [email protected] 135 Spread of measurements 04/13/2005 2 2 2 * 2 2 2 ( , ) ( ) ( , ) 2 x x t x x x t dx x x x x x x ∞-∞ ∆ = Ψ- Ψ =- + =- ∫ 2 2 * 2 2 ˆ ˆ ( , )( ) ( , ) , x x x x x x x p x t p p x t dx p p p i ∞ ∂ ∂-∞ ∆ = Ψ- Ψ =- = - ∫ ! 2 2 2 2 2 * 2 2 2 ˆ ˆ ( , )( ) ( , ) , ( ) m x E x t E E x t dx E E E V x ∞ ∂ ∂-∞ ∆ = Ψ- Ψ =- =- ∫ 2 2 2 * ) , ( ) ˆ ( ) , ( A A dx t x A A t x A- = Ψ- Ψ =...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

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05_04_13 - [email protected] 134 Expectation...

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