hw5246sol - 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. Liboff, problem 6.16, p. 180. 2. Liboff, problem 6.18, p. 180. 3. Liboff, problem 6.23, p. 182. 4. Liboff, problem 6.30, p. 185. 5. Liboff, problem 6.32, p. 186. 6. Liboff, 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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