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Results tagged with commutator
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user 83478
A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.
2
votes
Accepted
Why does equal commutator relation imply equal operator?
But we already know that the commutator is proportional to $b$ and thus we can evaluate the commutator trivially. In case of $\Ket{n_m}=\Ket{n_l}=\Ket{0}$, its simply the vacuum expectation value. … So it is true that $H_f$ is completely determined by the commutator. Now we want to write the Hamiltonian in terms of the bosonic creation and annihilation operator. …
- 506
2
votes
Accepted
What is the Significance of $\hat{N}$ and the Raising/Lowering operators not Commuting?
Take the case of $[\hat{N},\hat{a^\dagger}]=\hat{a}^\dagger$.
Operate it on an eigen state of $\hat{N}$, ie $\hat{N}|n>=n|n>$.
So
$(\hat{N}\hat{a^\dagger}-\hat{a^\dagger}\hat{N})|n>=\hat{a^\dagger …
- 506