All Questions
21
questions
0
votes
1
answer
602
views
What h.c. stands for?
I came across the following equation
$$ A = UAV + h.c. $$
For example, please see Eqn (2) in here.
But I have no idea what h.c. stands for... It seems that it comes from some physics.
Any comments ...
- 1,964
18
votes
5
answers
6k
views
Quantum mechanical books for mathematicians
I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential ...
- 2,400
0
votes
0
answers
249
views
Looking for an introductory text to quantum physics
I'm looking for an introductory but mathematically rigorous introduction to quantum physics. Ideally, it would be written for someone with a great deal of mathematical sophistication but no great ...
user279406
1
vote
0
answers
34
views
Reference request: "mathematical systems for probability"
This question is in response to an answer here on Physics.SE, but is essentially about math.
Consider the following quote from the linked-to answer above:
There are basically two kinds of ...
- 21.3k
9
votes
1
answer
2k
views
Complementary text for mathematical Quantum Mechanics lectures
I'm looking for a text to complement Frederic Schuller's lectures on QM. His approach is very mathematical -- in fact it looks like the first 12 of 21 lectures are just about the mathematical ...
- 2,730
3
votes
1
answer
829
views
Introductory book on probability for physicists
I'm a physics student looking to start learning more about probability. Is there some introductory book on measure theoretical probability theory that includes sections on quantum probability? To ...
- 31
3
votes
0
answers
64
views
Covariance of nonlinear sde
My problem is to compute the covariance of the following Ito process
$$
dX_t=AX_t+\sum_{k=1}^{n}B_kX_tdW_k,
$$
where $A,B_k$ are nonlinear operators defined on a complex separable Hilbert space $H$.
...
- 349
10
votes
1
answer
814
views
Derivation of Schrödinger's equation
I recall a famous quote of the late physicist Richard Feynman:
Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.
This quote ...
- 1,500
21
votes
7
answers
14k
views
Mathematics needed in the study of Quantum Physics
As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
- 3,210
1
vote
0
answers
53
views
Short examples that are/are not quantum-ergodic
Are there any considerably short examples of manifolds that are/aren't quantum ergodic, or quantum unique ergodic?
Note that a (compact) Riemannian manifold is said to be quantum ergodic if almost ...
- 377
10
votes
1
answer
1k
views
Category Theory and Quantum Mechanics
I am wondering if particle interactions in quantum theory can be modeled as a morphism between $2$ categories.
My reasoning is that since the states of particles are modeled as vectors in a Hilbert ...
- 369
19
votes
2
answers
4k
views
Prerequisite for Takhtajan's "Quantum Mechanics for Mathematicians"
I want to know the math that is required to read Quantum Mechanics for Mathematicians by Takhtajan.
From the book preview on Google, I gather that algebra, topology, (differential) geometry and ...
- 199
8
votes
1
answer
349
views
How to find interesting operators for a quantum system?
How can we find "interesting" operators for a quantum mechanical system?
I can think of the following method: Given some system with an associated Hilbert space $V$ and Hamiltonian $H:V\rightarrow V$,...
- 29.9k
2
votes
1
answer
589
views
Functional analysis and Quantum Mechanics
I am presently doing a course on functional analysis. I have done courses on quantum mechanics before. I see that many functional analysis books have an ending chapter on quantum mechanics.
So are ...
- 229
3
votes
0
answers
190
views
The intuition behind a matrix of a Hamiltonian?
We have derived an elegant partition function for a problem which resembles a quantized model taking the particles to be Bosons. The related Hamiltonian for every $i$th ensemble is there:
$$H_i=\sum_{...
- 4,310