Solving The Schrodinger Equation Has Everything Been Tried
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| Author | : Paul L. A. Popelier |
| Publisher | : World Scientific |
| Total Pages | : 375 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 1848167253 |
The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?
| Author | : Paul Popelier |
| Publisher | : World Scientific |
| Total Pages | : 375 |
| Release | : 2011-08-25 |
| Genre | : Science |
| ISBN | : 1908977760 |
The Schrödinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrödinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?/a
| Author | : F.A. Berezin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 573 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401131546 |
This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.
| Author | : Daniel A. Fleisch |
| Publisher | : Cambridge University Press |
| Total Pages | : 237 |
| Release | : 2020-02-20 |
| Genre | : Mathematics |
| ISBN | : 1108834736 |
A clear guide to the key concepts and mathematical techniques underlying the Schrödinger equation, including homework problems and fully worked solutions.
| Author | : Steven Holzner |
| Publisher | : John Wiley & Sons |
| Total Pages | : 339 |
| Release | : 2013-01-09 |
| Genre | : Science |
| ISBN | : 111846088X |
Your plain-English guide to understanding and working with the micro world Quantum Physics For Dummies, Revised Edition helps make quantum physics understandable and accessible. From what quantum physics can do for the world to understanding hydrogen atoms, readers will get complete coverage of the subject, along with numerous examples to help them tackle the tough equations. Compatible with classroom text books and courses, Quantum Physics For Dummies, Revised Edition lets students study at their own paces and helps them prepare for graduate or professional exams. Coverage includes: The Schrodinger Equation and its Applications The Foundations of Quantum Physics Vector Notation Spin Scattering Theory, Angular Momentum, and more Quantum physics — also called quantum mechanics or quantum field theory — can be daunting for even the most dedicated student or enthusiast of science, math, or physics. This friendly, concise guide makes this challenging subject understandable and accessible, from atoms to particles to gases and beyond. Plus, it's packed with fully explained examples to help you tackle the tricky equations like a pro! Compatible with any classroom course — study at your own pace and prepare for graduate or professional exams Your journey begins here — understand what quantum physics is and what kinds of problems it can solve Know the basic math — from state vectors to quantum matrix manipulations, get the foundation you need to proceed Put quantum physics to work — make sense of Schrödinger's equation and handle particles bound in square wells and harmonic oscillators Solve problems in three dimensions — use the full operators to handle wave functions and eigenvectors to find the natural wave functions of a system Discover the latest research — learn the cutting-edge quantum physics theories that aim to explain the universe itself
| Author | : Santanu Saha Ray |
| Publisher | : CRC Press |
| Total Pages | : 269 |
| Release | : 2018-11-13 |
| Genre | : Mathematics |
| ISBN | : 0429771789 |
This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.
| Author | : Erwin Schrödinger |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821835246 |
The famous equation that bears Erwin Schrödinger's name encapsulates his profound contributions to quantum mechanics using wave mechanics. This third, augmented edition of his papers on the topic contains the six original, famous papers in which Schrödinger created and developed the subject of wave mechanics as published in the original edition. As the author points out, at the time each paper was written the results of the later papers were largely unknown to him. This edition also contains three papers that were written shortly after the original edition was published and four lectures delivered by Schrödinger at the Royal Institution in London in 1928. The papers and lectures in this volume were revised by the author and translated into English, and afford the reader a striking and valuable insight into how wave mechanics developed.
| Author | : Ajit Thakkar |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 134 |
| Release | : 2017-10-03 |
| Genre | : Science |
| ISBN | : 1681746387 |
This book provides non-specialists with a basic understanding ofthe underlying concepts of quantum chemistry. It is both a text for second or third-year undergraduates and a reference for researchers who need a quick introduction or refresher. All chemists and many biochemists, materials scientists, engineers, and physicists routinely user spectroscopic measurements and electronic structure computations in their work. The emphasis of Quantum Chemistry on explaining ideas rather than enumerating facts or presenting procedural details makes this an excellent foundation text/reference. The keystone is laid in the first two chapters which deal with molecular symmetry and the postulates of quantum mechanics, respectively. Symmetry is woven through the narrative of the next three chapters dealing with simple models of translational, rotational, and vibrational motion that underlie molecular spectroscopy and statistical thermodynamics. The next two chapters deal with the electronic structure of the hydrogen atom and hydrogen molecule ion, respectively. Having been armed with a basic knowledge of these prototypical systems, the reader is ready to learn, in the next chapter, the fundamental ideas used to deal with the complexities of many-electron atoms and molecules. These somewhat abstract ideas are illustrated with the venerable Huckel model of planar hydrocarbons in the penultimate chapter. The book concludes with an explanation of the bare minimum of technical choices that must be made to do meaningful electronic structure computations using quantum chemistry software packages.
| Author | : Shan Gao |
| Publisher | : Cambridge University Press |
| Total Pages | : 201 |
| Release | : 2017-03-16 |
| Genre | : Science |
| ISBN | : 1107124352 |
Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.
| Author | : Arnold F. Nikiforov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 439 |
| Release | : 2006-02-09 |
| Genre | : Science |
| ISBN | : 3764373466 |
This book studies the widely used theoretical models for calculating properties of hot dense matter. Calculations are illustrated by plots and tables, and they are compared with experimental results. The purpose is to help understanding of atomic physics in hot plasma and to aid in developing efficient and robust computer codes for calculating opacity and equations of state for arbitrary material in a wide range of temperatures and densities.
