Relativistic Quantum Mechanics. Wave Equations

Book Description

Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.This third edition has been slightly revised to bring the text up-to-date.

Customer Reviews:

many typos and mistakes.......2006-07-27

This book is well written. Detail explanation is given for derivation step by step. There is space in the pages to take notes for your understandings.

There has been good discussions in previous reviews. I add some more aspects.

I went through all the pages and detected many typos and mistakes. Some are difficult to find such as page 210 and 288.

The book is self contained and will be good practice. However, I suggest to have someone to work on this book together. It may be just due to a typo even if you don't follow a context.

Comment.......2002-09-01

A word of caution, esp. in light of Alberto's review: There is no consistent "relativistic quantum wave mechanics"; there is only relativistic quantum field theory. Greiner's approach is archaic. Atomic physicists, who generally deal with only nonrelativistic electrons and nuclei, must use quantum field theory for the electromagnetic field. (See any modern book on quantum optics.) It is not just particle physicists who need field theory, and the fact that you can come away thinking otherwise is an unfortunate consequence of Greiner's old-fashioned approach.

Outstanding presentation - My highest recommendation.......2001-06-22

This book is THE book to use for any graduate quantum mechanics course. Most graduate programs in the country make the mistake of rushing their graduate QM courses into quantum field theory. This decision is made possible only by sacrificing the advanced non-relativistic QM (say, at the level of Schiff) and introductory relativistic QM (at the level of this book) that is necessary in order to really understand QFT.

This book fights that trend by covering in detail the topics that are thrown by the wayside in the traditional coverage, spending (investing?) page after page on topics that barely merit an exercise or a footnote in more traditional treatements. As just one example, Dirac's equation is solved for the square potential well and for the hydrogenic atom in full detail, without resorting to the usual "standard methods can be used to show that..."

This book is not a replacement to Bjorken & Drell or Itzykson & Zuber; what it does (and does well) is to cover the material that those books don't cover properly (or at all) because their mission is a different one. It belongs on the bookshelf of every physicist or physics student who was denied the opportunity to really master this material before jumping into quantum field theory. They can self-teach it using this book; I did.

The only serious issues with the book are the very large number of typos (but the reader who is following the discussion will have no problem spotting these) and the poor binding from which pages fall out after heavy use (and you will be giving the book a lot of use).

mathematically clear instructive textbook........2000-02-17

this is a part of greiner's theoretical physics series. this physics series have been used as a standard textbook in many schools, and its original german editions have been educating generations of german physicists. except for some problem in the translations, this physics series is excellent.

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It's everything you've ever wanted to know about quantum.
An Easy and comprehansive introduction to the subject
numerical methods for particles in a box?

Advanced Quantum Mechanics
Franz Schwabl
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540259015

Book Description

Advanced Quantum Mechanics, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic fields. Characteristic of Schwabl’s work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. This text extends and complements Schwabl’s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. New material has been added to this third edition of Advanced Quantum Mechanics on Bose gases, the Lorentz covariance of the Dirac equation, and the ‘hole theory’ in the chapter "Physical Interpretation of the Solutions to the Dirac Equation."

Customer Reviews:

It's everything you've ever wanted to know about quantum........2006-04-15

This is one of my favorite books. The writing is clear and concise, the mathematics aren't abused, the notation is simple and inviting, and the results are very important. This book is a vast improvement over the first volume, and it can (thankfully) be used completely independently of Volume I. The treatment of multi-particle systems is one of the best I've ever seen. This book is perfect for self-study (and this is good, since I don't usually see many course offerings covering this material).

The book is outstanding but, unfortunately, Springer seems to have committed itself to a perpetual decline in the quality of its books. Every copy of this particular edition that I've come across seems to have a loose binding. I haven't been able to find any differences between this edition and the older editions, so if you need to pick up a copy of this book (and any mathematician or physicist needs this book!) you might pick up an old edition instead (they're still available, new, on Amazon).

An Easy and comprehansive introduction to the subject.......1999-11-05

This book consists of three parts. Part1 begins with an introduction on the many body theory and introducing the idea of second quantization. Part2 focuses on relativistic quantum mechanics through relativistic wave equations. The last part is an introduction to quantum field theory using some results from part2. The simple presentation of the subject and the detailed math involved makes this book a comfortable one for a begginer.

numerical methods for particles in a box?.......1999-09-17

Well to tell you the truth actually , your book is a complete study about quantum mechanics ....

Book Description

The Dirac Equation is a modern presentation of the relativistic quantum mechanics of electrons intended to make new mathematical results accessible to a wider audience. It treats in some depth the relativistic invariance of a quantum theory, self-adjointness and spectral theory, qualitative features of relativistic bound and scattering states, and the external field problem in quantum electrodynamics, without neglecting the interpretational difficulties and limitations of the theory. A novel feature is the extensive use of supersymmetric quantum mechanics in the discussions of, e.g. the nonrelativistic limit, Fredholm and Witten indices, the relativistic Coulomb problem, particles with anomalous moments, behaviour in the presence of magnetic fields, and soliton theory. The book is aimed at scientists and graduate students interested in quantum mechanics who want to learn about the mathematical foundations, the physical interpretation and important applications of Dirac's electron theory.

Exact Solutions of Relativistic Wave Equations (Mathematics and its Applications)

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Excellent Referrence!

Exact Solutions of Relativistic Wave Equations (Mathematics and its Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 079230215X

Customer Reviews:

Excellent Referrence!.......2000-03-02

An excellent reference for Dirac and Shrodinger operators in reletive mechanics! The Kerr Geometry represented is excellent, and the solutions given are helpful both for reference and perhaps for further research!

Generalized Hamiltonian Formalism for Field Theory: Constrait Systems

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Generalized Hamiltonian Formalism for Field Theory: Constrait Systems
G. Sardanashvily
Manufacturer: World Scientific Pub Co Inc
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ASIN: 9810220456

Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory

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Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory

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Book Description

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

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very good
A good overview
Learn to apply your quantum mechanics

Intermediate Quantum Mechanics
Hans Albrecht Bethe , and Roman Jackiw
Manufacturer: Perseus Books (Sd)
ProductGroup: Book
Binding: Paperback

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ASIN: 0805307575

Book Description

Graduate students in both theoretical and experimental physics will find this third edition of Intermediate Quantum Mechanics, refined and updated in 1986, indispensable. The first part of the book deals with the theory of atomic structure, while the second and third parts deal with the relativistic wave equations and introduction to field theory. Throughout its nearly thirty-five years in print, Intermediate Quantum Mechanics has consistently offered more complete coverage of applications of quantum mechanics than any other single-volume work on the subject.

Customer Reviews:

very good.......2004-03-03

This is a very useful book, but only for someone with a solid grasp of QM at the undergrad level. The only problem is the terrible type in which the equations are set. Why Addison-Wesley released a new edition without fixing this is beyond me.
(profit, perhaps? No, never on a scholarly textbook.)

A good overview.......2003-01-31

That quantum mechanics must be understood by anyone working in any area of technology is now well accepted. Indeed, semiconductor device physics, proteomics, and computational chemistry are just three of the more modern areas where a through knowledge of quantum mechanics is needed in order to make any kind of significant progress. This book, written by two of the major players in the development of quantum mechanics in the 20th century, is an excellent overview of how to do practical computations in quantum mechanics. The book is addressed primarily to the aspiring atomic physicist and spectroscopist, but it could serve well anyone interested in the applications of quantum mechanics, such as those in the aforementioned fields. Due to space limitations, I will only review the first 8 chapters of the book.

Chapter 1 is a brief overview of elementary quantum mechanics, and the authors set down the notation and units to be followed in the book. They state the main goal of the book, which is to solve the Schrodinger equation for an atom with nuclear charge Ze. This problem for one-electron is straightforwardly solved, but for more than one electron approximation techniques must be used, a few of which they mention. Since spin will have to be dealt with throughout the book, the authors include a description of spin 1/2 particles.

In chapter 2 the authors discuss the use of symmetry principles in quantum many-particle systems, pointing out the origin of exchange degeneracy and the Pauli exclusion principle. The authors also give an interesting discussion of the experimental determination of symmetry, particularly their argument for the absence of hidden variables.

In chapter 3 the authors give an overview of the quantum mechanics of two-electron atoms, pointing out that the calculations give six-figure agreement between theory and experiment. Perturbation and variational methods are used to solve the Schrodinger equation for this system, and show the origin of the triplet and singlet levels for the helium atom.

In chapter 4, the authors introduce another approximation technique, the self-consistent field or "Hartree-Fock" method, in order to calculate the excited states for the two-electron atom more efficiently. This approach involves using a variational trial function, called the determinantal wave function, as an ansatz, which because of orthogonality and parity considerations, results in a set of equations, called the Hartree-Fock equations, for the single electron orbitals. The "exchange term" in these equations is discussed in detail, involving a notion of a "nonlocal" potential. The physical significance of the eigenvalue in these equations is also discussed, and related to the famous Koopman theorem. It is proven also that atoms with closed shells leads to a spherically symmetric theory. The periodic table is shown to be a consequence of the Pauli principle and the Hartree-Fock calculation.

An improvement to Hartree-Fock, the Thomas-Fermi method, which does not include exchange, is discussed in chapter 5. Classified as a "statistical method", this method finds the effective potential energy experienced by a small test charge, along with the electron density around the nucleus. The authors show how exchange effects can be included using a procedure due to P.A.M. Dirac, which uses a concept of effective exchange potential, and one due to W. Lenz, which is a constrained optimization procedure, requiring that the total energy be stationary.

In order to remove the degeneracy in the atomic shells due to the Hartree-Fock approximation, the authors view it as a perturbation expansion in chapter 6, with the unperturbed Hamiltonian being the Hartree-Fock central field Hamiltonian, and the perturbation being the electrostatic interaction of the electrons minus a suitable average of it. The search for proper linear combinations of zero-order degenerate eigenfunctions to make the total Hamiltonian diagonal entails the use of the total orbital and spim angular momentum of all the electrons in the atom. Hence the authors outline in detail how to perform the addition of angular momenta in this chapter. The reader can see clearly the origin of the famous Clebsch-Gordon coefficients. This program is carried out in more detail in chapter 7, wherein the authors considers and atom which has an electron configuration distributed over several complete and one incomplete shell. The incomplete shell gives several different degenerate solutions, and this degeneracy can be removed by the assignment of angular momentum and spin quantum numbers to the orbitals in the shell. This chapter is characterized by a considerable amount of arithmetic in computing matrix elements, which can readily be handled by modern symbolic computation packages.

The contribution of the spin-orbit interaction to the level structure of atoms, ignored in the previous two chapters, is studied in chapter 8. The authors also consider the interaction of the electron configuration with an external field, such as a magnetic field. The spin-orbit interaction is not considered in a relativistic framework, but instead is given a "pseudo-derivation", in the words of the authors. The (correct) Dirac theory for spin-orbit interaction is given later in chapter 22. And here again, the matrix elements, and reduced matrix elements, considered in this chapter can best be handled by symbolic computation packages. This is particularly true for matrix elements of vector operators between states of different angular momentum, which the authors shy away from. The reader though can see the origin of the famous Wigner-Eckart theorem in the context of these computations. The Zeeman effect, resulting from the interaction of an electron with a homogeneous magnetic field, is discussed, along with the Paschen-Back effect, which results from the external magnetic field being strong enough to allow the Zeeman term in the Hamiltonian to dominate the spin-orbit interaction. Also discussed is the Stark effect, which results when an atom is placed in an external electric field. The authors show how to compute the energy shifts in this case, using, but not proving, some formulas due to Condon and Shortly.

Learn to apply your quantum mechanics.......1998-08-19

The "Intermediate" of the title means that you are supposed to have learned your basic QM in a book such as Griffiths' "Introduction to Quantum Mechanics" . Bethe's text then leads you to those parts of QM most successful in applications, especially in atomic structure. The treatment of perturbation theory is very clean, simple and effective. The semi-classical theory of radiation is excellently described and then, in perhaps the best part of the book, is used to review Einstein's derivation of Planck's equilibrium distribution of radiation, explaining the need for spontaneous emmission and motivating the treatment of quantum electrodynamics, outlined at the end of the text. This is a great book. What else could one expect from Hans Bethe, the man who discovered how the Sun produces its energy?

Relativistic Quantum Mechanics, Wave Equations

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Relativistic Quantum Mechanics, Wave Equations
Walter Greiner
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback
ASIN: B000H0HZME

Unitary Representations of the Poincare Group and Relativistic Wave Equations

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Unitary Representations of the Poincare Group and Relativistic Wave Equations
Y. Ohnuki
Manufacturer: World Scientific Pub Co Inc
ProductGroup: Book
Binding: Hardcover

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ASIN: 997150250X

The Weyl-Dirac Theory and Our Universe (In Contemporary Fundamental Physics - Valerie V. Dvoeglazov - Editor)

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The Weyl-Dirac Theory and Our Universe (In Contemporary Fundamental Physics - Valerie V. Dvoeglazov - Editor)
Mark Israelit
Manufacturer: Nova Science Publishers
ProductGroup: Book
Binding: Library Binding

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ASIN: 1560726903

Book Description

The aim of the present book is very simply stated; it is to discuss - and to some extent to explore - the Weyl-Dirac theory in connection with classical electromagnetism and cosmology. The study of our universe in recent years has become one of the most interesting and important subjects. Current cosmology considers a large number of various subjects from elementary particles to the large scale-structure of the universe. In order to explain this variety of phenomena, which occur between the Planck time and tens of billions of years, one makes use of methods stemming from different physical theories: elementary particle physics, quantum mechanics, thermodynamics, statistical physics, celestial mechanics, etc. It is, however, generally accepted to express those approaches in terms of the general theory of relativity, which is based on Riemann's geometry. In this book, it is shown that some unexplained cosmological and electrodynamic phenomena may be treated and understood in the geometrically based framework of Weyl and Dirac.

The book is intended for physicists, astrophysicists, cosmologists and mathematicians who are familiar with the foundations of Einstein's general theory of relativity.

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