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Unformatted text preview: University of Colorado, Department of Physics PHYS3220, Fall 09, HW#4 due Wed, Sep 16, 2PM at start of class 1. (Griffiths, problem 1.7, 15 pts) Prove the Ehrenfest theorem d < p x > dt =  V x (1) where the potential V is a real quantity. (This theorem tells us that expectation values obey classical laws.) 2. The three expressions xp x , p x x and ( xp x + p x x ) / 2 are equivalent in classical mechanics. The corresponding quantum mechanical operators are X P x , P x X and ( X P x + P x X ) / 2. Show that X P x and P x X are not Hermitian operators, but ( X P x + P x X ) / 2 is a Hermitian operator. (15 pts). Hint: To show that an operator A is Hermitian, check if < A > = < A > * , where A is the operator assigned to the observable A . 3. In classical mechanics all quantities obey the rules of ordinary algebra, e.g. the commu tation rule. The previous problem has shown that operators in quantum mechanics in general do not commute with each other. Thus, ifgeneral do not commute with each other....
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
 Fall '08
 STEVEPOLLOCK
 Physics

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