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5.6 (a) Let Q be an operator which is not a function of time, and let H be the Hamiltonian operator. Show that მ ih(q) = ([Q, H]) Ət Here (q) is the expectation value of Q for an arbitrary time- dependent wave function V, which is not necessarily an eigenfunc- tion of H, and [Q, H]) is the expectation value of the commutator of Q and H for the same wave function. This result is known as Ehrenfest's theorem. (b) Use this result to show that მ (p) = It av მე What is the classical analog of this equation?

5.6 (a) Let Q be an operator which is not a function of time, and let H be the Hamiltonian operator. Show that მ ih(q) = ([Q, H]) Ət Here (q) is the expectation value of Q for an arbitrary time- dependent wave function V, which is not necessarily an eigenfunc- tion of H, and [Q, H]) is the expectation value of the commutator of Q and H for the same wave function. This result is known as Ehrenfest's theorem. (b) Use this result to show that მ (p) = It av მე What is the classical analog of this equation?

Modern Physics
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter6: Quantum Mechanics In One Dimension
Section: Chapter Questions
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5.6 (a) Let Q be an operator which is not a function of time, and let H be the Hamiltonian operator. Show that მ ih(q) = ([Q, H]) Ət Here (q) is the expectation value of Q for an arbitrary time- dependent wave function V, which is not necessarily an eigenfunc- tion of H, and [Q, H]) is the expectation value of the commutator of Q and H for the same wave function. This result is known as Ehrenfest's theorem. (b) Use this result to show that მ (p) = It av მე What is the classical analog of this equation?
Transcribed Image Text:5.6 (a) Let Q be an operator which is not a function of time, and let H be the Hamiltonian operator. Show that მ ih(q) = ([Q, H]) Ət Here (q) is the expectation value of Q for an arbitrary time- dependent wave function V, which is not necessarily an eigenfunc- tion of H, and [Q, H]) is the expectation value of the commutator of Q and H for the same wave function. This result is known as Ehrenfest's theorem. (b) Use this result to show that მ (p) = It av მე What is the classical analog of this equation?
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