Tagged Questions
4
votes
3answers
548 views
Canonical Commutation Relations
Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the ...
2
votes
2answers
368 views
Operator relation involving the logarithm of an operator?
Dirac gives the relation: $\exp(iaq)f(q,p) = f(q, p - a\hbar)\exp(iaq)$ where $\hbar$ is Planck's constant. Can anybody give me the corresponding relation when the $\exp$ function is a $\ln$?
25
votes
4answers
1k views
Trace of a commutator is zero - but what about the commutator of $x$ and $p$?
Operators can be cyclically interchanged inside a trace:
$${\rm Tr} (AB)~=~{\rm Tr} (BA).$$
This means the trace of a commutator of any two operators is zero:
$${\rm Tr} ([A,B])~=~0.$$
But what about ...
