hw5246 - there is also a quantum analog to the virial...

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Physics 246, Spring 2007 Homework #5 Due in class, Wednesday, March 7, 2007 Feel free to discuss the problems with me and/or each other. Each student must write up his/her own solutions separately. Each problem is worth 10 points unless otherwise indicated. 1. Libo±, problem 6.16, p. 180. 2. Libo±, problem 6.18, p. 180. 3. Libo±, problem 6.23, p. 182. 4. Libo±, problem 6.30, p. 185. 5. Libo±, problem 6.32, p. 186. 6. Libo±, problem 6.33, p. 186. 7. Just as Ehrenfest’s theorem gives an analog to the classical equations of motion,
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Unformatted text preview: there is also a quantum analog to the virial theorem, which relates the expec-tation values of the kinetic and potential energies. Prove the quantum analog for a stationary state in one dimension, i.e. show that for a stationary state, 2 h KE i = h x ∂V /∂x i where KE is the kinetic energy. ( Hint: Recall that in a stationary state, expec-tation values of operators are constant in time. Consider the operator ˆ x ˆ p and the relation of its time derivative to its commutator with the Hamiltonian.)...
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