All Questions
Tagged with quantum-mechanics reference-request
14
questions with no upvoted or accepted answers
3
votes
0
answers
170
views
Understanding the free will theorem
I am trying to understand the mathematical content of the free will theorem. See this link or just the wikipedia pages and the references therein.
I think the main point of the theorem is the ...
- 2,719
3
votes
1
answer
86
views
Reference request for quantum Teichmuller space
I would like to ask for some detailed reference for quantum Teichmuller theory, better in a mathematical taste. I read a little bit on Kashaev's or Chekhov and Fock's, but find that I need to fill ...
- 749
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
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:
$$H_i=\sum_{...
- 4,310
2
votes
0
answers
108
views
Spectrum of $H = - \Delta + y^2 + a e^{b(x+y)}$.
Define the Hamiltonian
$$
H = - \Delta + y^2 + a e^{b(x+y)}\,,
$$
where $- \Delta = - \partial_x^2 - \partial_y^2$ and $a,b > 0$. I'm trying to determine the spectrum and/or generalized ...
- 2,949
1
vote
0
answers
43
views
Quantum Mechanical PDE Question
I'm studying quantum mechanics and I'm considering the usual time-independent Schrödinger equation
\begin{equation*}
-\left(\frac{\hbar^{2}}{2m}\right)\left(\nabla'\right)^{2}u_{E}(\mathbf{x}') + V(\...
- 11
1
vote
0
answers
80
views
Computing Complex Ito calculus for stochastic process
Let $X_t$ be a stochastic process in $\mathbb{C}^n$ such that
$$ dX_t = a(X_t,t)dt + b(X_t,t)dW_t.$$
And let $f:\mathbb{C}^n \to \mathbb{C}$.
Then how to compute $df(X_t)$ in complex?
If $f$ is a ...
- 1,964
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
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
1
vote
0
answers
64
views
Three body problem with point interactions
I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials).
Is ...
- 11
1
vote
0
answers
34
views
References for three body problems with Fermi statistic
I'm studying the three body problem with two fermions of unitary mass and another different particle. I need references of the HVZ theorem in this case. Is there someone who knows them?
- 51
0
votes
0
answers
60
views
Are there any theorems that can only be explained by analogies requiring knowledge of quantum mechanics?
The theorems I’ve seen in analysis can be explained by analogies that invoke the macroscopic visible world, areas, volumes, life sized physical things in sets. Are there any theorems in math that if ...
user739402
0
votes
0
answers
249
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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