Of(adsbygoogle = window.adsbygoogle || []).push({}); Modern Quantum Mechanics. This starts with a Hamiltonian

[itex]

H = a(|1\rangle\langle 1| - |2\rangle\langle 2| + |1\rangle\langle 2| + |2\rangle\langle 1|)

[/itex]

This has eigenvalues [itex]\pm a\sqrt{2}[/itex]. Shouldn't a Hamiltonian have only non-negative eigenvalues? If the sign in front of the [itex]|2\rangle\langle 2|[/itex] is [itex]+[/itex] instead of a [itex]-[/itex] you get eigenvalues [itex]0[/itex] and [itex]2a[/itex], which makes more sense (assuming a is real and positive). So might this be a typo, or am I wrong in general about the eigenvalues of a Hamiltonian? Or am I taking this toy "Hamiltonian" too seriously?

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# Sakurai problem 1.9.

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