All Questions
25 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
573
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 \...
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 ...
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 ...
4
votes
1
answer
469
views
Is there any book that treat time-dependent perturbation theory with rigorous mathematics?
I am searching for rigorous mathematics books or notes for time dependent perturbation theory.
For introductory quantum mechanics there is the excellent book spectral theory and quantum mechanics ...
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
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
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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 ...
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
3
answers
210
views
References for examples of $\ast$-algebra approach to QM and QFT
In studying QFT on curved spacetime I've found the $\ast$-algebra approach as one viable approach to the subject on the paper Quantum Fields in Curved Spacetime by Wald.
The $\ast$-algebra approach ...
2
votes
1
answer
2k
views
Functional Analysis for Quantum Mechnanics [duplicate]
I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time.
Can someone suggest some books? I like books with ...
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
1
answer
2k
views
Continuous spectrum of hydrogen atom
I wonder if there is a nice treatment of the continuous spectrum of hydrogen atom in the physics literature--showing how the spectrum decomposition looks and how to derive it.
1
vote
0
answers
107
views
Can anybody recommend a book on quantum physics for a mathematically minded student? [duplicate]
Basically what the title says. I'm a math/physics double major going into my second year, but I'm much more math oriented. I'll be taking a quantum class in the fall and I'd like a book that ...
5
votes
0
answers
237
views
References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?
Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus.
In a sense, in a similar way the Lebesgue integral (or ...
3
votes
2
answers
1k
views
A rigorous treatment of distributions in quantum mechanics
In many introductory courses to quantum mechanics, we see $\delta$-functions all over the place. For example when expressing an arbitrary wave function $\psi(x)$ in the basis of eigenfunctions of the ...
3
votes
1
answer
188
views
Mathematical Physics SUSY QM Resource Recommendation
I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM.
Does anybody know whether ...
3
votes
1
answer
2k
views
What is the mathematical background needed for quantum physics? [duplicate]
I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
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.
5
votes
3
answers
571
views
Quantum Mechanics in terms of *-algebras
I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefore started reading:
Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
18
votes
5
answers
12k
views
A book on quantum mechanics supported by the high-level mathematics
I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
8
votes
4
answers
8k
views
Path integral formulation of quantum mechanics
I'm a mathematics student with not much background in physics. I'm interested in learning about the path integral formulation of quantum mechanics. Can anyone suggest me some books on this topic with ...
4
votes
4
answers
9k
views
Mathematical background for Quantum Mechanics [duplicate]
What are some good sources to learn the mathematical background of Quantum Mechanics?
I am talking functional analysis, operator theory etc etc...
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?