All Questions
7
questions
0
votes
1
answer
107
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Mathematical meaning of a position eigenbra $\langle x_0 |$
Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$.
For $f\in L^...
- 3,350
3
votes
1
answer
290
views
Mathematical definition of annihilation and creation operators
I am self-studying quantum field theory and have gotten to creation and annihilation operators, respectively denoted $A^\dagger$ and $A$. Conceptually I understand what these objects are, at least on ...
- 3,350
0
votes
1
answer
364
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Radial position operator
While trying to find the expectation value of the radial distance $r$ of an electron in hydrogen atom in ground state the expression is:
$$\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \...
- 1,270
0
votes
0
answers
54
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Inner product evaluation in QM
On wikipedia on the page for inner product it states that for any two $x,y$ in a vector space $V$ the inner product $(\cdot , \cdot)$ satisfies $(ax, y) = a(x,y)$ where $a\in\mathbb{C}$.
The inner ...
- 73
4
votes
2
answers
500
views
Completeness of Norm in Hilbert Space
I am not sure what it really means for the norm to be complete in a Hilbert Space. Can you provide me a proper definition? I am aware of the formula $||\Psi|| = <\Psi|\Psi>^{1/2}$.
What are ...
- 43
3
votes
2
answers
432
views
Precise definition of the Hilbert space in QM?
In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
- 131
4
votes
3
answers
597
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Why does Griffiths define the complex inner product differently? [closed]
I have just now noticed that Griffiths (in his book Introduction to Quantum Mechanics) defines the complex inner product as
$$\big<z,w\big>~=~\sum_{i=1}^n\overline{z}_iw_i.$$
In all ...
- 236