Homework9 - Physics 401 Homework#9 1 Time evolution of...

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Physics 401 - Homework #9 1) Time evolution of expectation values (three points each). If an observable (A) has a quantum mechanical operator ( A ˆ ) which does not depend on time, then the time-rate change of the expectation value of that observable in any arbitrary state is given by   A H i dt A d ˆ , ˆ a) Apply the result shown above to the case where the observable (A) is the momentum. Let the Hamiltonian for the system be that of a particle moving in an arbitrary one-dimensional potential function V(x) . What famous law of classical physics does this result correspond to? b) If the expectation value for an observable is constant in time, we say that that observable is conserved. Suppose we have a free particle (V(x) = constant). Is momentum conserved? Is energy conserved? c)) Suppose we have a non-free particle (V(x) constant). Is momentum conserved? Is energy conserved? 2)
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This note was uploaded on 12/29/2011 for the course PHYSICS 401 taught by Professor Hall during the Fall '11 term at Maryland.

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Homework9 - Physics 401 Homework#9 1 Time evolution of...

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