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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