All Questions
3
questions
5
votes
1
answer
191
views
Problem on a rank 1 perturbation of an self-adjoint operator
With my teacher we have been trying to solve for a while a problem that consists of two parts, and each one in three sections. The first part, which has to do with the problems that I was able to ...
- 160
2
votes
1
answer
105
views
Consequences of Deficiency indices theorem (Von Neumann theory)
Let $T: \operatorname{dom}(T) \rightarrow \scr H$ be a symmetric operator.
$T$ admits self-adjoint extensions $\iff$ $d_+ = d_-$, where $d_\pm = \dim \ker(T^\dagger \pm i \mathbb{I})$
If $d_+ = d_-$,...
- 141
3
votes
2
answers
751
views
Expectation value of pure state in quantum mechanics
It's well known that in quantum mechanics, the expectation value of a self-adojint operator $A$ in pure state $|\psi\rangle$ is $\langle\psi |A|\psi\rangle = \operatorname{Tr}(A |\psi \rangle \...
- 310