5.7 (a) Show that the one-dimensional momentum operator is Hermi- tian. (b) Use this result to show that the one-dimensional Hamiltonian operator H with potential V(x) is Hermitian. What (reasonable) assumption must be made about V(x) to derive this result?

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.30P
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5.7 (a) Show that the one-dimensional momentum operator is Hermi-
tian.
(b) Use this result to show that the one-dimensional Hamiltonian
operator H with potential V(x) is Hermitian. What (reasonable)
assumption must be made about V(x) to derive this result?
Transcribed Image Text:5.7 (a) Show that the one-dimensional momentum operator is Hermi- tian. (b) Use this result to show that the one-dimensional Hamiltonian operator H with potential V(x) is Hermitian. What (reasonable) assumption must be made about V(x) to derive this result?
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