3
votes
1answer
42 views

Equivalent definitions for strictly positive elements

We have two usual definitions for strictly positive elements in C*-algebras: Let $A$ be a C*-algebra Definition (a) [MURPHY, C$^*$-algebras and Operator Theory] An element $a\in A_+$ is said to be ...
0
votes
1answer
443 views

Dot products in commutators

Suppose $\hat r$ is an position operator, $\hat p$ is a momentum operator and $\vec c$ is a constant vector. What does the commutator $[\hat p, \vec c\cdot\hat r]$ mean? I see that you can expand ...
3
votes
1answer
112 views

Clarification on Dirac notation

I am new to the Dirac notation, so would appreciate some clarification. Suppose $\Psi=\psi_1+\psi_2$ where $\Psi$ is normalized and $H$ is a linear operator such that $H\psi_1=E_1\psi_1$ and ...