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Is every eigenvalue of the Hamiltonian a form of energy? If not are there values of the Hamiltonian that do not correspond to the energy of the system?

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  • $\begingroup$ The Hamiltonian operator is the energy operator of the quantum system. Its eigenvalues are the energy eigenvalues of the system. $\endgroup$ – Gert Feb 16 at 23:38
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The physical interpretation of the eigenvalues of $H$ is that they are the possible outcomes of measuring the energy of your system. The eigenvalues obviously have units of energy.

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