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2 votes
0 answers
79 views

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
575 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 ...
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
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 ...
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.
6 votes
1 answer
318 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
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.
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?