Solvable One Dimensional Multi State Models For Statistical And Quantum Mechanics
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| Author | : Rajendran Saravanan |
| Publisher | : Springer Nature |
| Total Pages | : 186 |
| Release | : 2021-11-14 |
| Genre | : Science |
| ISBN | : 9811666547 |
This book highlights the need for studying multi-state models analytically for understanding the physics of molecular processes. An intuitive picture about recently solved models of statistical and quantum mechanics is drawn along with presenting the methods developed to solve them. The models are relevant in the context of molecular processes taking place in gaseous phases and condensed phases, emphasized in the introduction. Chapter 1 derives the arisal of multi-state models for molecular processes from the full Hamiltonian description. The model equations are introduced and the literature review presented in short. In Chapter 2, the time-domain methods to solve Smoluchowski-based reaction-diffusion systems with single-state and two-state descriptions are discussed. Their corresponding analytical results derive new equilibrium concepts in reversible reactions and studies the effect of system and molecular parameters in condensed-phase chemical dynamics. In Chapter 3, time-domain methods to solve quantum scattering problems are developed. Along side introducing a brand new solvable model in quantum scattering, it discusses transient features of quantum two-state models. In interest with electronic transitions, a new solvable two-state model with localized non-adiabatic coupling is also presented. The book concludes by proposing the future scope of the model, thereby inviting new research in this fundamentally important and rich applicable field.
| Author | : A.G Ushveridze |
| Publisher | : CRC Press |
| Total Pages | : 480 |
| Release | : 2017-07-12 |
| Genre | : Science |
| ISBN | : 1351420321 |
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.
| Author | : Rodney J. Baxter |
| Publisher | : Elsevier |
| Total Pages | : 499 |
| Release | : 2016-06-12 |
| Genre | : Science |
| ISBN | : 1483265943 |
Exactly Solved Models in Statistical Mechanics
| Author | : Sergio Albeverio |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 506 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 0821836242 |
"This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered. The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided. The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988."--Résumé de l'éditeur.
| Author | : Bill Sutherland |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 398 |
| Release | : 2004-06-21 |
| Genre | : Science |
| ISBN | : 9813102144 |
This invaluable book provides a broad introduction to the fascinating and beautiful subject of many-body quantum systems that can be solved exactly. The subject began with Bethe's famous solution of the one-dimensional Heisenberg magnet more than 70 years ago, soon after the invention of quantum mechanics. Since then, the diversity and scope of such systems have been steadily growing.Beautiful Models is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in physics. It is also suitable for the non-experts in physics who wish to have an overview of some of the classic and fundamental models in the subject. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
| Author | : Christopher King |
| Publisher | : World Scientific |
| Total Pages | : 234 |
| Release | : 1997-02-26 |
| Genre | : |
| ISBN | : 9814546593 |
This volume contains the proceedings of the conference on 'Exactly Soluble Models in Statistical Mechanics: Historical Perspectives and Current Status', held at Northeastern University in March 1996 — the first ever conference to deal exclusively with this topic. Besides invited presentations by leading researchers in the field, the conference held a session of contributed papers by participants from throughout the world. The proceedings, which include both the invited and the contributed papers, reflect the broad range of interest in exactly soluble models as well as the diverse fields in physics and mathematics that they connect. Apart from providing concise and timely reviews, the papers in this volume give a snapshot of the current state of affairs. The topics covered range from a historical survey of the field (by E H Lieb) to the latest formulation of a star-star transformation of spin models (by R J Baxter).
| Author | : Yongmin Cho |
| Publisher | : World Scientific |
| Total Pages | : 278 |
| Release | : 1997-04-01 |
| Genre | : |
| ISBN | : 9814546321 |
Recently, exciting new notions have been emerging in theoretical physics. The quantum nature of gravitation revealed in the physics of black holes, exotic excitations obeying fractional statistics, and integrable structure such as Yangian symmetry in low-dimensional models are some of the subjects presented in this volume.The spectrum of the talks at the School, reflected in the proceedings, is a wide one ranging from the phenomenology of particle physics to that of condensed matter physics, to topics of a mathematical nature. This is an indication that there is a robust interplay of ideas from diverse disciplines of theoretical physics in the Asia-Pacific region.
| Author | : Mo-lin Ge |
| Publisher | : World Scientific |
| Total Pages | : 186 |
| Release | : 1995-05-31 |
| Genre | : |
| ISBN | : 9814549754 |
This volume covers the recent developments of the exact solvable models, Yangian symmetry, the long-ranged interaction models and high-dimensional integrable systems. The authors are all experts in their fields. The volume provides a systematic introduction to statistical and mathematical physics and contains review papers and other contributions.
| Author | : Tohru Eguchi |
| Publisher | : World Scientific |
| Total Pages | : 546 |
| Release | : 1995-05-11 |
| Genre | : |
| ISBN | : 9814549908 |
The topics discussed in this volume are: Symmetry and Foundations in Classical and Quantum Mechanics; Geometry, Topology and Quantum Field Theory; Quantum Groups and Infinite-Dimensional Lie Algebras; Algebraic Approach to Nuclear Structure; Integrable Statistical Systems and Theory of Critical Phenomena Supersymmetry; Atomic and Molecular Physics; Condensed Matter Physics; Other Applications of Group Theory to Physics.
| Author | : |
| Publisher | : Academic Press |
| Total Pages | : 392 |
| Release | : 1997-03-20 |
| Genre | : Science |
| ISBN | : 0080582532 |
Advances in Quantum Chemistry publishes surveys of current developments in the rapidly developing field of quantum chemistry--a field that falls between the historically established areas of mathematics, physics,chemistry, and biology. With invited reviews written by leading international researchers, each presenting new results, this quality serial provides a single vehicle for following progress in this interdisciplinary area. "Volume 28 collects papers written in honor of Geerd H.F. Diercksen. Diercksen is a pioneer in the field of quantum mechanics whose research includes studies of the structure and stability of hydrogen-bonded and Van der Waals dimers and small clusters, thevibrational and rotational spectra of diatomic and triatomic molecules, on static electric properties in solutions and of molecules absorbed on surfaces. His results are essential in molecular and atomic physics, in astrophysics, and in biochemistry.
