All Questions
30 questions
2
votes
0
answers
79
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Quantum Mechanics book with good treatment on unbounded operators [duplicate]
I'm looking for a certain kind of approach to quantum mechanics. In most places I've looked, almost all of the exposition on how to employ construct observables in quantum mechanics is that of compact ...
9
votes
0
answers
576
views
Nuclear spectral theorem in Rigged Hilbert Spaces (Gelfand-Maurin theorem)
Before I go into the question, I would like to mention that I am a physicist with some formal mathematical knowledge, but not expert in functional analysis.
In physics, we very often say: Let $|x \...
0
votes
0
answers
63
views
Reference for mathematics of quantum mechanics with infinite degrees of freedom?
I am looking for a book, or lecture notes or even courses available on YouTube where there is a good and detailed discussion on the mathematical aspects of Quantum Mechanics with infinite degrees of ...
0
votes
0
answers
109
views
References on the difference between Dirac's and Von Neumann's approach to Quantum Mechanics (rigged Hilbert Space vs Hilbert Space only)
I have not found any clear and comparative explanation between the Dirac and von Neumann versions of Quantum Mechanics (rigged Hilbert Space vs Hilbert Space only). I have found some short articles. ...
1
vote
0
answers
34
views
Question about the operators in quantum mechanics [duplicate]
I am confused about the operators in quantum mechanics and even the way they are used, their symbols, etc. Is there any book or anything that I can study so that I can fully understand them before ...
2
votes
1
answer
319
views
Recommendations for Algebraic quantum mechanics book
I am familiar with quantum mechanics and quantum information at the level of Sakurai and Preskill's lecture notes / Nielsen and Chuang. I want to study the $C^*$ algebraic formulation of quantum ...
0
votes
0
answers
37
views
What are the best quantum mechanic books that focus on the Dirac notation and linear algebra? [duplicate]
I have a little bit of a hard time following the Dirac notation and the mathematics that follow it. Are there any textbooks that focus on the math only?
0
votes
0
answers
86
views
Good reference for block-diagonalization via discrete symmetry?
It's common knowledge among physicists that when you have a linear Hermitian operator like a quantum Hamiltonian that commutes with symmetry matrices you can then block-diagonalize Hermitian operator ...
2
votes
1
answer
94
views
What is best book on self-adjoint extensions?
I need to understand self-adjoint extensions in quantum mechanics to solve some problems of scattering and bound states in Aharonov-Bohm potentials. There are some referencies that present the math ...
0
votes
0
answers
40
views
Text reference for linear Stark Effect
I was trying to study the linear stark effect and an example of the splitting of $2S\pm2P_z$ orbitals, described here. Can someone suggest to me a reference for the similar material discussed but in ...
-1
votes
2
answers
269
views
Which publication did Dirac introduce the "Associative axiom of multiplication" in?
I want to know which publication to cite when I reference the "Associative axiom of multiplication" in the Bra-Ket notation of Quantum mechanics. Sakurai only attributes it to Dirac, but doesn't name ...
2
votes
2
answers
125
views
Reference for variational characterization of quantum trace distance in infinite dimensions
Consider two density matrices $\rho$ and $\sigma$. It is well known that for finite-dimensional systems, the trace distance $\frac{1}{2}\Vert \rho-\sigma \Vert_1$ has the variational characterization
$...
0
votes
0
answers
56
views
Can someone suggest some good resources to study "Addition of angular momentum"?
Please help me out in finding some good resource to study Addition of angular momentum of quantum mechanics mechanics part in detail which also explains all the mathematics involved.
3
votes
1
answer
211
views
References of Deficiency indices theorem (von Neumann)
I am looking for proof or some interpretation around why the domain of the new extension $D(A_U)$ in the Theorem below is given by its specific formula.
I have already searched in papers and here but ...
1
vote
3
answers
433
views
Hilbert space and group theory: relationship between these two approaches to quantum mechanics, and references for a beginner?
I have read basic books on Quantum Mechanics like R. Shankar's "Introduction to Quantum Mechanics, Griffiths "Quantum Mechanics" and partly I followed Bransden "Atoms and Molecules".
But none of the ...
1
vote
0
answers
63
views
Recommended books for introduction to Quantum Mechanics for students who are mathematically aligned [duplicate]
I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
1
vote
0
answers
414
views
Book recommendation on Quantum Mechanics which is a bit mathematically aligned and gives good introduction to Hilbert Space for beginners [duplicate]
I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
2
votes
1
answer
203
views
What are some good resources to learn Vector Spaces for Quantum Mechanics?
I am currently using Shankar's Principles of Quantum Mechanics. I had no trouble understanding finite dimension vector spaces using it. But I find it difficult to understand infinite dimensional ...
5
votes
1
answer
217
views
Reference Request: Basis-independent formulation of tensor networks
I could not find any references for a basis-independent formulation of tensor networks: All papers I have found use pretty much (explicitly or implicitly) the canonical computational basis by defining ...
1
vote
1
answer
253
views
Spectral theorem for unbounded self-adjoint (hermitian) operators
It is my understanding that in quantum mechanics we use self-adjoint operators (that is an axiom of the theory). This operators can be either bounded or unbounded, being the latter the more general ...
1
vote
0
answers
146
views
What are some resources for Algebraic quantum mechanics for Physicists
I am interested in the GNS construction and other stuff. I am aware of Valter Moretti's book but I want something that is more inclined towards physicists.
3
votes
0
answers
77
views
How to build QM with projective spaces from the beginning?
In conventional treatment of QM, one assumes that (1) physical states are normalized vectors in (rigged) Hilbert spaces and (2) operators correspond to observables, with their eigenvectors denoting ...
2
votes
0
answers
724
views
Which is a good and short book for foundations of quantum mechanics? [duplicate]
I am looking for a book that has stuff on quantum states, entanglement, etc.
I am aware of the book, Geometry of Quantum States.
I have read Ballentine's book, Quantum Mechanics: A modern development
0
votes
0
answers
38
views
I wasn't able to find a good resource for Bipartite state and Bell's theorem
Our professor used tensor product to explain bipartite operator and states and then he used the new operator and state to explain Bell theorem. I wasn't able to find a good resource or reference for ...
1
vote
1
answer
663
views
Configuration Space And Hilbert Space For A Physicist Without Knowledge Of Analysis
I have passed calculus course, have basic knowledge of complex numbers and passed introductory linear algebra course. I am trying to study Griffith Quantum Mechanics book, but I am also checking some ...
3
votes
2
answers
359
views
Quantum cloning of orthonormal states
If I understand correctly, for two orthonormal states
$\left|\psi_1\right\rangle$ and $\left|\psi_2\right\rangle$
in the Hilbert space H, there must exist a unitary
transformation $U$, such that:
$$U\...
3
votes
3
answers
540
views
Koopmann von Neumann (KvN) Theory
I was just wondering does anyone have any informative sources apart from the obvious wikipedia articles regarding Koopmann von Neumann (KvN) theory? Or if its possible could someone explain the basic ...
50
votes
2
answers
9k
views
Rigged Hilbert space and QM
Are there any comprehensive texts that discuss QM using the notion of rigged Hilbert spaces? It would be nice if there were a text that went through the standard QM examples using this structure.
14
votes
3
answers
1k
views
Hilbert-Schmidt basis for many qubits - reference
Every density matrix of $n$ qubits can be written in the following way
$$\hat{\rho}=\frac{1}{2^n}\sum_{i_1,i_2,\ldots,i_n=0}^3 t_{i_1i_2\ldots i_n} \hat{\sigma}_{i_1}\otimes\hat{\sigma}_{i_2}\otimes\...
8
votes
3
answers
4k
views
Books for linear operator and spectral theory
I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me?