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When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and use Einstein's relation $E=mc^2$ to derive the energy?

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The details are probably dependent on how you actually create your model of the harmonic oscillator system, no? – user758556 Sep 2 '13 at 22:21

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