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13 votes

On commutator of bounded operators

If $H$ is finite dimensional there is a one-line solution: ${\rm tr}(JK - KJ) = 0$, so $JK - KJ$ cannot have positive spectrum. But it is false in general! Let $V$ be a partial isometry from $H$ onto ...
Nik Weaver's user avatar
  • 42.4k
4 votes

When is this operator positive semi-definite?

Too long for an additional comment. I guess that you can keep the assumption $\hat P, \hat Q$ Hermitian and require $$ [\hat P, \hat Q]=1/(2πi), $$ as it is the case with the prototypical example $ \...
Bazin's user avatar
  • 15.3k
6 votes
Accepted

Quantum probabilistic method?

The Hilbert-Polya approach to the Riemann hypothesis follows this path, by attempting to relate the zeroes of the Riemann zeta function to a quantum mechanical scattering problem. The probability ...
Carlo Beenakker's user avatar

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