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I've just finished a discussion with my peers and lecturer on some of the postulates of QM,

My lecturer said that "the total energy of any quantum mechanical system is always given by the Hamiltonian, which may be obtained by appropraite application of the classical Hamiltonian"

I took issue with this, there are examples within classical mechanics where the Hamiltonian is conserved but the total energy of a system isn't. I therefore fail to see how the Hamiltonian can always represent the total energy of QM system.

Am I completely off the mark here?

Kind regards

Barny

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# Hamiltonian and total energy

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