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Integral over operators equal -When are operators equal?
This is a physics motivated question from quantum mechanics. When I have two operators $\hat{A}$ and $\hat{B}$ acting on the Hilbertspace $\mathbb{C}-L^2(\mathbb{R})$ with
$$\int\psi^*(x)\hat{A}\psi(x)...
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Deficiency index of symmetric operator is locally constant
Let $A: D_A \rightarrow H$ be a symmetric linear operator defined on $D_A \subseteq H$. Define the deficiency index of $A$ at $z \in \mathbb{C} \setminus \mathbb{R}$ to be $\dim( \ker (A^* - \bar{z}))$...
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Proving Uniqueness of Momentum Operator
I'm attempting to do two things. One making a well posed question, and two answering that question.
Here is the question: I'm trying to show that the operator $- i \frac{\partial }{ \partial x } $ ...
- 17.5k