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nomadreid
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This is a basic question, so probably easy to answer. The following from Wikipedia seems pretty standard while describing the Schrödinger equation: "...and Ĥ is the Hamiltonian operator (which characterises the total energy of the system under consideration)."
On the other hand, from page 100 of Patrick Hamill's "A Student's Guide to Lagrangians and Hamiltonians", he states "... there are situations in which the Hamiltonian is not the total energy of the system."
If I accept both of these, my logical conclusion would be that the situations which Schrödinger's equation describes is not one of the situations which Hamill is referring to. The other possibility is that Wikipedia is over-simplifying. Which conclusion is correct?
The closest post I could find here on this question, https://www.physicsforums.com/threads/hamiltonian-and-total-energy.266410/, either did not answer this question, or the answer was not clear to me, which is why I am posting a new thread.
On the other hand, from page 100 of Patrick Hamill's "A Student's Guide to Lagrangians and Hamiltonians", he states "... there are situations in which the Hamiltonian is not the total energy of the system."
If I accept both of these, my logical conclusion would be that the situations which Schrödinger's equation describes is not one of the situations which Hamill is referring to. The other possibility is that Wikipedia is over-simplifying. Which conclusion is correct?
The closest post I could find here on this question, https://www.physicsforums.com/threads/hamiltonian-and-total-energy.266410/, either did not answer this question, or the answer was not clear to me, which is why I am posting a new thread.