Let's say we have operator X that is Hermitian and we have operator P that is Hermitian. Is the following true:(adsbygoogle = window.adsbygoogle || []).push({});

[X,P]=ihbar

This is the commutator of X and P.

This particular result is known as the canonical commutation relation.

Expanding:

[X,P]=XP-PX=ihbar

This result indicates that XP[itex]\neq[/itex]PX because XP-PX[itex]\neq[/itex]0

Because XP[itex]\neq[/itex]PX, XP is not a Hermitian operator.

Likewise, because PX[itex]\neq[/itex]XP, PX is not a Hermitian operator.

So to summarize:

The commutator implies multiplication of operators

Multiplication of Hermitian operators does not always produce another Hermitian operator.

If two Hermitian operators do not commute, then their product is not Hermitian.

Any mistakes here?

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# How to determine the product of two Hermitian operators is Hermitian

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