If $\psi$ acting on $a_+$ and $a_-$ operator just moves up and down the ladder, why is $[a_-, a_+] = 1$ and not 0?
65724
Why Don't the Ladder Operators Commute?
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
154772
The Momentum Operator in QM
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
86125
If $A$ is idempotent, then the eigenvalues of $A$ are $0$ or $1$
92744
These two operators commute...but their eigenvectors aren't all the same. Why?
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
93550
How to find the matrix representation of an operator from its action on a basis?
21290
Meaning of $\int \phi^\dagger \hat A \psi \:\mathrm dx$
144019
A strictly positive operator is invertible
94717
Systems in quantum mechanics solved by ladder operator method
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
27482
How to show $-\sup(-A)=\inf(A)$?
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.