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05_04_20

# 05_04_20 - 149 Expectation values for px Review of one...

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[email protected] 149 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 04/20/2005 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 ) (

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[email protected] 150 Spread of measurements 04/20/2005 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
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05_04_20 - 149 Expectation values for px Review of one...

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