## New answers tagged quantum-mechanics

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 ...

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
$
\...

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 ...

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