# Tagged Questions

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### Virasoro Operators commutation relations

For the commutation relation in quantising the bosonic string $\left[L_n,L_{m}\right]=(n-m)L_{n+m}+\frac{D}{12}n(n^2-1)\delta_{n+m,0}$ we can then calculate this for $m=-n$ in between the vacuum ...
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### Commutator of Momentum with a Position dependent function

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
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### Why does $[xp_{y},x]$ commute?

I'm looking at a solution in my book that says $[xp_{y},x]$ commutes. Does bracket notation imply: $[A,B]=AB-BA$ so that $[xp_{y},x]=xp_{y}x-xxp_{y}$ Taking the comment from Max Graves and ...
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### Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
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### Are higher order mixed partial derivatives of wave function with different ordination equal?

For example, given two operators: $$A = \frac{\partial}{\partial x}+\frac{\partial}{\partial y},$$ $$B =\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2} + 1.$$ Deriving commutator ...
### Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities
I've been trying to derive the relation $$[\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k$$ without doing each permutation of ${x,y,z}$ individually, but I'm not really getting anywhere. ...