Lect11_XandP2 - Lecture 11: X and P, part II PHY851/fall...

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Lecture 11: X and P, part II PHY851/fall 2009
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Quick review:
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The constant C is found from normalization: This leads to the results: h h h h / / 2 1 2 1 ipx ipx e p x x p e p x = = = π Normalization
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The momentum operator But we have really learned even more. By the same logic we must have: So when we say: We really mean: In fact, this is all you need to remember ψ x dx d i x x P x x d P x h = = dx d i P h = x dx d i P x h = i.e., let While you can argue that its meaning might be understandable, my point is just that it is not proper use of Dirac notation. I think that a correct statement would be: x dx d x dx i P = h This is now clearly an operator in Hilbert space, whose meaning is precisely defined by the definition of the derivative. It then seems reasonable to represent the r.h.s. as: dX d i P h = In analogy to: x x V x dx i X V ) ( ) ( = h
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`Coordinate Representation If we make a decision to work in x-basis only,
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This note was uploaded on 12/21/2011 for the course PHY 851 taught by Professor Moore,m during the Fall '08 term at Michigan State University.

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Lect11_XandP2 - Lecture 11: X and P, part II PHY851/fall...

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