All Questions
Tagged with quantum-mechanics reference-request
47
questions
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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
3
votes
2
answers
132
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General definition of POVM
Wikipedia gives the following definition of positive operator-valued measure (POVM):
A POVM on a measurable space $(X,M)$ is a function $F$ defined on $M$ whose values are bounded non-negative self-...
- 759
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1
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187
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Mathematical Foundations of Quantum Mechanics
As the title says, I am interested in a textbook/reference that deals exclusively with the mathematical foundations of quantum mechanics, without (or, with minimal) physics involved.
As an example on ...
- 103
3
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170
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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
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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
3
votes
2
answers
354
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Extension of Choi-Jamiolkowski isomorphism to not completely positive maps
In quantum physics, the concept of Channel-State duality is of prime importance in understanding the final state of the system after passing through a channel or performing quantum operations. The ...
- 587
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2
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1k
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Schrödinger equation involving the Dirac-Delta
I am taking a course on quantum mechanics and I try to understand the time-independent Schrödinger-equation with the Delta-potential:
$$\frac{-\hslash^2}{2m}\psi''(x)-V_0\delta(x)\psi(x)=E\psi(x)$$
...
- 2,436
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3
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Mathematically rigorous Quantum Mechanics
I am a student of mathematics attending a course in Quantum Mechanics. This course is held by a physicist, and it is really confusing for me to follow his reasonments. With this, I do not mean to be ...
- 2,532
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1
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Reference request for operator theory in Quantum mechanics
I am studying Shankar's Principles of Quantum Mechanics. In the first chapter where the author introduces the necessary mathematics tool for QM, the concept of derivatives of operators with respect to ...
- 999
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3
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190
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Reference request: representation focused view of quantum mechanics
I'm interested in learning a bit more about quantum mechanics from a more Lie algebra/representation theoretic perspective, hopefully including but not going past quantum field theory.
I was ...
- 1,903
3
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1
answer
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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
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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
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1
answer
602
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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
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1
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214
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Hilbert space theory and their applications
What are the best books that discuss the theory of Hilbert spaces and their applications to quantum mechanics for the beginners
- 2,508
6
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676
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Quantum Chemistry book recommendation. [closed]
I am trying to learn quantum chemistry. I have an extensive background in math and physics, so I'm looking for a book that makes full use of whatever physics and mathematics is relevant to this ...
- 69
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1
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Is there a book on the purely mathematical version of perturbation theory?
Is there a book on the purely mathematical version of perturbation theory, or all current references just in relation to applied fields like statistics and quantum mechanics? I remember first coming ...
- 131
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The Mathematics of Quantum Mechanics? [duplicate]
I have asked this question in the physics.stackexchange.com forum too - sorry if that is a no-no; I feel it straddles the boundary between the two, and similar questions have been answered rather ...
- 1,524
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3
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Books on Perturbation Methods
I am having problems finding descent books on perturbation methods. I am looking for a book which covers; asymptotic expansions, matched Asymptotic expansions, Laplace's Method, Method of steepest ...
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0
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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
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5
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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
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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
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0
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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
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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
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1
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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 ...
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Baker Campbell Hausdorff formula for unbounded operators
Baker Campbell Hausdorff formula says that for elements $X,Y$ of a Lie algebra we have
$$e^Xe^Y=\exp(X+Y+\frac12[X,Y]+...),$$
which for $[X,Y]$ being central reduces to
$$e^Xe^Y=\exp(X+Y+\frac12[X,Y])....
- 121
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0
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64
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Covariance of nonlinear sde
My problem is to compute the covariance of the following Ito process
$$
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
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2
answers
2k
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Linear algebra references for a deeper understanding of quantum mechanics
I'm a graduate student studying quantum mechanics/quantum information and would like to consolidate my understanding of linear algebra. What are some good math
books for that purpose?
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1
answer
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Books on random permutations
I'm looking for books or introductory/expository articles about random permutations, in particular with regards to their cycle structure.
EDIT: I forgot to mention that I'm especially interested in ...
- 11.5k
10
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1
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814
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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
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2
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Book on periodic Schrödinger operators
I am looking for good books about the spectral theory of periodic (1-dimensional) Schrödinger operators on a compact interval.
A good reference I found was Reed/Simon Analysis of Operators (and a ...
user66906
21
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7
answers
14k
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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
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0
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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
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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
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1
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304
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Reference request for differential geometry/quantum chaos text
I'm looking for a differential-geometry based exposition of chaos theory and quantum chaos. Ideally, it would start with the Hamiltonian formalism (on symplectic manifolds) and discuss as many of the ...
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19
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2
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4k
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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 ...
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349
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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$,...
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2
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1
answer
589
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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 ...
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190
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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
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4
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383
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Which book to read on quantum-related mathematics
Recently I watched the "Big Bang Theory" and decided to google about quantum mechanics. It really intrigued me. But I also understood that I am too stupid to understand even the basic mathematics in ...
- 1,313
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0
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495
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Is quantum game theory reducible to classical game theory? [closed]
Modnote: This question was manually migrated (closed and crossposted) to MathOverflow by request of the OP.
Quantum game theory is an extension of classical game theory to the quantum domain. It ...
- 3,220
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2
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751
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Expectation value of pure state in quantum mechanics
It's well known that in quantum mechanics, the expectation value of a self-adojint operator $A$ in pure state $|\psi\rangle$ is $\langle\psi |A|\psi\rangle = \operatorname{Tr}(A |\psi \rangle \...
- 310
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0
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64
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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 ...
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1
answer
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Translation of an article
I need to read this article
"On the spectrum of an energy operator for atoms with fixed nuclei in subspaces corresponding to irriducible representations of permutation groups"
authors:G.Zhislin, A. ...
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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?
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3
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Studying quantum mechanics without physics background
I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics.
I posted this question in physics stackexchange, but there doesn'...
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Example for projective geometry used in quantum mechanics
In the book The Road to Reality by Roger Penrose, projective geometry as developed during the Renaissance is framed as (eventually) playing a pivotal role in quantum mechanics. (In fact, Penrose seems ...
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3
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Quantum mechanics for mathematicians
I'm looking for books about quantum mechanics (or related fields) that are written for mathematicians or are more mathematically inclined.
Of course, the field is very big so I'm in particular ...