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Saturday, May 16, 2020 | History

2 edition of Self-adjoint Extensions As a Quantization Problem (Progress in Mathematical Physics) found in the catalog.

Self-adjoint Extensions As a Quantization Problem (Progress in Mathematical Physics)

Dmitry Gitman

# Self-adjoint Extensions As a Quantization Problem (Progress in Mathematical Physics)

## by Dmitry Gitman

Written in English

Subjects:
• Theoretical methods,
• Applied,
• Mathematical Analysis,
• Mathematics,
• Science/Mathematics

• The Physical Object
FormatHardcover
Number of Pages246
ID Numbers
Open LibraryOL11388111M
ISBN 100817644008
ISBN 109780817644000
OCLC/WorldCa144521663

Self-adjoint extensions in quantum mechanics: general theory and applications to Schrödinger and Dirac equations with singular potentials. [D M Gitman; I V Ti︠u︡tin; B L Voronov] the book shows how problems associated with correct definition of observables can be treated Read more Rating: (not yet rated) 0 with reviews - Be the. 2 A Caterina, Fiammetta, Simonetta Whether our attempt stands the test can only be shown by quantitative calculations of simple systems Max Born, On Quantum Mechanics.

This paper is concerned with second-order linear difference equations with complex coefficients which are formally J-symmetric. Both J-self-adjoint subspace extensions and J-self-adjoint operator extensions of the corresponding minimal subspace are completely characterized in terms of boundary conditions. MSCA70, 47ACited by: 2. This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any 6 Self-adjoint Extensions of the Laplacian on a Locally At the end of the introduction of both volumes there is a list of books that may be. theory.. Lectures on the Mathematics of Quantum Mechanics I, Atlantis Studies in Mathematical File Size: 4MB.

Problem M.5 Let A be a normal matrix. Let λ be an eigenvalue of A and V the eigenspace of A of eigenvalue λ. Prove that V is the eigenspace of A∗ of eigenvalue λ¯. Problem M.6 Let A be a normal matrix. Let v and w be eigenvectors of A with diﬀerent eigenvalues. Prove that v ⊥ w. Problem M.7 Let A be a self-adjoint matrix. Prove that a File Size: 55KB. Abstract. Given a unitary representation of a Lie group G on a Hilbert space H, we develop the theory of G-invariant self-adjoint extensions of symmetric operators both using von Neumann’s theorem and the theory of quadratic also analyze the relation between the reduction theory of the unitary representation and the reduction of the G-invariant unbounded operator.

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### Self-adjoint Extensions As a Quantization Problem (Progress in Mathematical Physics) by Dmitry Gitman Download PDF EPUB FB2

Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment.

The necessary mathematical background is then built by developing the theory of self-adjoint by: springer, Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis.

Though a “naïve” treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded. Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment.

The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the nave treatment.

It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical Brand: Birkhäuser Boston.

struction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to o er a brief account of some recent ideas in the theory of self-adjoint extensions of symmetric operators on Hilbert spaces and their applications to a few speci c problems in Quantum Mechanics.

Contents 1. Introduction 2 2. self-adjoint extensions that are compatible with the given symmetries. Concretely, if a symmetric operator is G-invariant in the sense of Eq.

(), then it is clear that not all self-adjoint extensions of the operator will also be G-invariant. This is evident if one xes the self-adjoint extension by selecting boundary conditions. the set of all possible self-adjoint extensions.

We have gathered in appendix A some technical details on the extensions of the momentum operator and in appendix B we discuss the spectra of the Hamiltonian operator for a particle in a box. A proof for parity preserving self-adjoint extension is given in Appendix Size: KB.

Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials (Hardcover) Average rating: 0 out of 5 stars Write a review D M Gitman; I V Tyutin; B L Voronov.

It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct.

Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials (Progress in Mathematical Physics Book 62) eBook: D.M.

Gitman, I.V. Tyutin, B.L. Voronov: : Kindle Store. Buy Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrodinger and Dirac Equations with Singular Potentials (Progress in Mathematical Physics) by D.

Gitman, I. Tyutin, B. Voronov (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces and singular by: The problem of constructing self-adjoint ordinary differential operators starting from self-adjoint differential operations is discussed based on the general theory of self-adjoint extensions of.

We call attention to the fact that quantization includes the problem of a correct definition of quantum-mechanical observables like Hamiltonian, momentum, etc. as self-adjoint operators in an appropriate Hilbert space.

This problem is nontrivial for systems on. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment.

It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. An application to the deformation quantization of one-dimensional systems with boundaries is also presented.

Bonneau, J. Faraut and G. Valent, Self-adjoint extensions of operators and the teaching of quantum mechanics, Am. Phys., 69 A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part I Cited by: Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials: D.M.

Gitman, I.V. Tyutin. Defining the self-adjoint extension of P is a procedure aimed at rendering D(P †) = D(P) by enlarging D(P) and restricting D(P †) so they coincide.

In particular, the condition (7) can also be fulfilled by imposing the boundary condition, (π) = e 2 π i α (− π), for a given α ∈[0,1), and thus we can enlarge the domain of P and. Going through the Quantum mechanics book by Capri, am time and again held with some stupid doubts on this topic of self-adjointness.

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. $\overline{A}$ is self-adjoint.

This also implies that $\overline{A}$ is the unique self. Vol. 58 () REPORTS ON MATHEMATICAL PHYSICS No. 2 RESOLVENTS OF SELF-ADJOINT EXTENSIONS WITH MIXED BOUNDARY CONDITIONS KONSTANTIN PANKRASHKIN Institut ftir Mathematik, Humboldt-Universit~it zu Berlin Rudower Chaus Berlin, Germany and D6partement de Math~matiques, Institut Galilee, Universit6 Paris 13 99 avenue J.-B.

C16ment, Cited by: Self-adjoint extensions in quantum mechanics: general theory and applications to Schrödinger and Dirac equations with singular potentials.

[D M Gitman; I V Ti︠u︡tin; B L Voronov] -- Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and.Self-adjoint Extensions in Quantum Mechanics starts by way of contemplating quantization difficulties quite often, emphasizing the nontriviality of constant operator development by way of providing paradoxes of the naïve remedy.

the mandatory mathematical heritage is then outfitted by means of constructing the speculation of self-adjoint /5(15).