Quasi Exactly Solvable Models in Quantum Mechanics

Quasi Exactly Solvable Models in Quantum Mechanics

Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear ...

Author: A.G Ushveridze

Publisher: Routledge

ISBN: 9781351420310

Category: Science

Page: 480

View: 631

Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.
Categories: Science

Panorama of Contemporary Quantum Mechanics

Panorama of Contemporary Quantum Mechanics

Quasi-Exactly Solvable Models in Quantum Mechanics. Briston: Institute of Physics; 1993 [40] Finkel F, Gonzalez-Lopez A, Rodriguez MA. On the families of orthogonal polynomials associated to the Razavy potential. Journal of Physics A: ...

Author: Trong Tuong Truong

Publisher: BoD – Books on Demand

ISBN: 9781839626654

Category: Science

Page: 108

View: 249

This book is devoted to recent developments in quantum mechanics. After an Introductory chapter, Chapter 2 describes the cooperative spontaneous lasing mechanism in gas in three level systems and their possible quantum retardation effects. Chapter 3 is concerned with the evolution of states of large quantum particle systems via marginal correlation operators. Chapter 4 studies the effects of electronic transfer using ab initio quantum calculation methods to access biological macromolecular system behaviors. Chapter 5 concentrates on new features of supersymmetric quantum mechanics using the adjunction of boson-fermion symmetry. The book will be of interest to graduate and Ph.D students as well as scientists from various backgrounds who are concerned with quantum effects.
Categories: Science

Lie Theory and Its Applications in Physics

Lie Theory and Its Applications in Physics

So we see that the problem of constructing the (separable) exactly or quasi-exactly solvable models of quantum mechanics is reduced to the problem of constructing hermitian exactly or quasi-exactly solvable multi-parameter spectral ...

Author: H-D Doebner

Publisher: World Scientific

ISBN: 9789814547086

Category:

Page: 284

View: 319

There is an apparent trend towards geometrization of physical theories. During the last 20 years, the most successful mathematical models for the description and understanding of physical systems have been based on the Lie theory in its widest sense and various generalizations, for example, deformations of it. This proceedings volume reflects part of the development. On the mathematical side, they report on representations of Lie algebras, quantization procedures, non-commutative geometry, quantum groups, etc. Furthermore, possible physical applications of these techniques are discussed (e.g. quantization of classical systems, derivations of evolution equations, discrete and deformed physical systems). This volume complements the book Generalized Symmetries in Physics, published by World Scientific in 1994. Contents:Representation Theory and Quantization MethodsNoncommutative Geometry, Quantum Algebras and Applications to Relativistic and Nonrelativistic SystemsSpecial Applications to Physical Systems and Their Generalized ModelsRepresentation Theory and Quantization Methods Readership: Mathematicians and physicists. keywords:
Categories:

Symmetry in Physics

Symmetry in Physics

G. Álvarez , F. Finkel , A. González - López , and M. A. Rodríguez , Quasi - exactly solvable models in nonlinear optics ... J. Bajer and A. Miranowicz , Sub - Poissonian photon statistics of higher harmonics : quantum predictions via ...

Author: Robert T. Sharp

Publisher: American Mathematical Soc.

ISBN: 0821870297

Category: Science

Page: 227

View: 242

Papers in this volume are based on the Workshop on Symmetries in Physics held at the Centre de recherches mathematiques (University of Montreal) in memory of Robert T. Sharp. Contributed articles are on a variety of topics revolving around the theme of symmetry in physics. The preface presents a biographical and scientific retrospect of the life and work of Robert Sharp. Other articles in the volume represent his diverse range of interests, including representation theoretic methods for Lie algebras, quantization techniques and foundational considerations, modular group invariants and applications to conformal models, various physical models and equations, geometric calculations with symmetries, and pedagogical methods for developing spatio-temporal intuition. The book is suitable for graduate students and researchers interested in group theoretic methods, symmetries, and mathematical physics.
Categories: Science

Non Hermitian Hamiltonians in Quantum Physics

Non Hermitian Hamiltonians in Quantum Physics

E2-Quasi-Exactly. Solvable. Model. The general notion [1, 2] underlying solvable Hamiltonian systems is that its Hamiltonian operatorsHacting on some graded space Vn asH : Vn → Vn preserves the flag structure V0 ⊂ V1 ⊂ V2 ⊂···⊂ Vn ...

Author: Fabio Bagarello

Publisher: Springer

ISBN: 9783319313566

Category: Science

Page: 403

View: 593

This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.
Categories: Science

Symmetries and Algebraic Structures in Physics Quantum field theory quantum mechanics and quantum optics

Symmetries and Algebraic Structures in Physics  Quantum field theory  quantum mechanics and quantum optics

QUASI - EXACT SOLUBILITY . NEW PHENOMENON IN QUANTUM MECHANICS A.G. Ushveridze Institute of Physics of the Georgian Academy of Sciences Tamarashvili str . ... The quasi - exactly solvable models have been discovered recently ( 3,4 ) .

Author: V. V. Dodonov

Publisher: Nova Science Pub Incorporated

ISBN: CHI:37721809

Category: Science

Page: 274

View: 215

Categories: Science

Group Theoretical Methods in Physics

Group Theoretical Methods in Physics

is shown in [ 5 ] to be normalizable and quasi - exactly solvable with respect to g , provided that the parameter 1 is large enough . ... ( 16 ) Ushveridze , A.G. , Quasi - exactly solvable models in quantum mechanics , Sov . J. Part .

Author: Mariano A. del Olmo

Publisher:

ISBN: MINN:31951P00836623B

Category: Group theory

Page: 496

View: 475

Categories: Group theory

Matematychni studi

Matematychni studi

Ushveridze A. G. Quasi - exactly Solvable Models in Quantum Mechanics . - Bristol : IOP Publishing , 1993 . 8. Finkel F. , González - López A. , Rodríguez M. A. Quasi - eractly solvable spin 1/2 Schrödinger operators // Preprint hep ...

Author:

Publisher:

ISBN: UOM:39015053959212

Category: Mathematics

Page:

View: 405

Categories: Mathematics

Symmetries and Algebraic Structures in Physics

Symmetries and Algebraic Structures in Physics

QUASI - EXACT SOLUBILITY . NEW PHENOMENON IN QUANTUM MECHANICS A.G. Ushveridze Institute of Physics of the Georgian Academy of Sciences Tamarashvili str . ... The quasi - exactly solvable models have been discovered recently ( 3,4 ) .

Author: V. V. Dodonov

Publisher:

ISBN: 1560720379

Category: Mathematical physics

Page:

View: 991

Categories: Mathematical physics

Eesti Teaduste Akadeemia Toimetised

Eesti Teaduste Akadeemia Toimetised

Fernández C. , D. J. and Rosu , H. C. On first - order scaling intertwining in quantum mechanics . Rev. Mexicana Fís . , 2000 , 46 ( suppl . 2 ) , 153–156 . 10. Ushveridze , A. G. Quasi - exactly Solvable Models in Quantum Mechanics .

Author:

Publisher:

ISBN: UOM:39015057385687

Category: Mathematical physics

Page:

View: 885

Categories: Mathematical physics