All Questions
4
questions
2
votes
1
answer
167
views
From the condition $[A,B]=A$, what can I say about $B$?
I'm struggling in understanding the meaning of this condition that I found in an operator equation:
\begin{equation}
[A,B]=A
\end{equation}
where both $A$ and $B$ are hermitian operators. What can I ...
- 123
2
votes
1
answer
639
views
Can we derive $N=aa^{\dagger}$ from these conditions?
Let $[a,b]:=ab-ba$ for all $a,b\in X$ a non commutative ring. Suppose that $a,a^{\dagger},N$ are operators satisfying
$$\begin{align}
[a,a^{\dagger}]&=1 \\
[N,a]&=-a \\
[N,a^{\dagger}] &= ...
- 15.3k
3
votes
0
answers
220
views
Pureness of Vector States
How does one show that irreducibility is equivalent to a vector state being pure?
In what follows I will fill in the details of the question: Let $\mathcal{H}$ denote a Hilbert space and let $\...
- 802
2
votes
1
answer
7k
views
Commutator relationship proof $[A,B^2] = 2B[A,B]$
I'm trying to find the condition necessary for this commutator relationship equality:
$$[A,B^2]=2B[A,B]$$
So far I've done this:
\begin{align*}
[A,B^2] & = B[A,B] + [A,B]B \\
&...
- 135