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Principles of Quantum Mechanics de R. Shankar

Principles of Quantum Mechanics

Autor R. Shankar
en Limba Engleză Hardback – 31 aug 1994

ABORDAREA PRACTICĂ: În Principles of Quantum Mechanics, R. Shankar propune o metodologie riguroasă care prioritizează fundamentul matematic înainte de orice incursiune în fenomenologia cuantică. Subliniem faptul că autorul alocă un spațiu generos — aproape șaptezeci de pagini — introducerii în spații vectoriale liniare și notației Dirac, asigurându-se că cititorul stăpânește aparatul formal necesar pentru a procesa postulatele ulterioare. Remarcăm o structură logică impecabilă: după consolidarea matematică, textul revizuiește conceptele cheie din mecanica clasică (formalismele Lagrangian și Hamiltonian), oferind contextul necesar pentru a înțelege de ce fizica clasică devine insuficientă la scară atomică. Cititorul care a aplicat ideile din A Mathematical Journey to Quantum Mechanics de Salvatore Capozziello va găsi aici o aprofundare tehnică superioară, unde rigoarea axiomatică se îmbină cu o pedagogie testată direct la catedră în universități precum Harvard și Yale. Această lucrare se înscrie organic în opera lui R. Shankar, completând viziunea sa din Basic Training in Mathematics; dacă acel volum pregătea terenul, Principles of Quantum Mechanics reprezintă construcția finală, fiind mult mai tehnic și mai dens decât seria sa introductivă Fundamentals of Physics. Progresia materialului este liniară, pornind de la operatori și probleme de autovalori spre aplicații complexe, menținând un echilibru constant între demonstrația formală și exercițiile aplicate, esențiale pentru nivelul de masterat sau doctorat.

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Specificații

ISBN-13: 9780306447907
ISBN-10: 0306447908
Pagini: 676
Ilustrații: XVIII, 676 p. 116 illus.
Dimensiuni: 183 x 260 x 43 mm
Greutate: 1.48 kg
Ediția:2nd edition
Editura: Springer Us
Locul publicării:New York, NY, United States

Public țintă

Graduate

De ce să citești această carte

Recomandăm acest volum studenților și cercetătorilor care doresc o înțelegere profundă, nu doar computațională, a fenomenelor cuantice. Câștigul principal este claritatea conceptuală oferită de tratarea axiomatică. Este un instrument de lucru esențial pentru oricine vrea să treacă de la nivelul descriptiv la cel de expertiză tehnică în fizica teoretică, beneficiind de experiența pedagogică a unui autor recunoscut pentru entuziasmul și rigoarea sa.

Descriere scurtă

R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:

- Clear, accessible treatment of underlying mathematics
- A review of Newtonian, Lagrangian, and Hamiltonian mechanics
- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates
- Unsurpassed coverage of path integrals and their relevance in contemporary physics
The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Cuprins

1. Mathematical Introduction.- 1.1. Linear Vector Spaces: Basics.- 1.2. Inner Product Spaces.- 1.3. Dual Spaces and the Dirac Notation.- 1.4. Subspaces.- 1.5. Linear Operators.- 1.6. Matrix Elements of Linear Operators.- 1.7. Active and Passive Transformations.- 1.8. The Eigenvalue Problem.- 1.9. Functions of Operators and Related Concepts.- 1.10. Generalization to Infinite Dimensions.- 2. Review of Classical Mechanics.- 2.1. The Principle of Least Action and Lagrangian Mechanics.- 2.2. The Electromagnetic Lagrangian.- 2.3. The Two-Body Problem.- 2.4. How Smart Is a Particle?.- 2.5. The Hamiltonian Formalism.- 2.6. The Electromagnetic Force in the Hamiltonian Scheme.- 2.7. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations.- 2.8. Symmetries and Their Consequences.- 3. All Is Not Well with Classical Mechanics.- 3.1. Particles and Waves in Classical Physics.- 3.2. An Experiment with Waves and Particles (Classical).- 3.3. The Double-Slit Experiment with Light.- 3.4. Matter Waves (de Broglie Waves).- 3.5. Conclusions.- 4. The Postulates—a General Discussion.- 4.1. The Postulates.- 4.2. Discussion of Postulates I -III.- 4.3. The Schrödinger Equation (Dotting Your i’s and Crossing your ?’s).- 5. Simple Problems in One Dimension.- 5.1. The Free Particle.- 5.2. The Particle in a Box.- 5.3. The Continuity Equation for Probability.- 5.4. The Single-Step Potential: a Problem in Scattering.- 5.5. The Double-Slit Experiment.- 5.6. Some Theorems.- 6. The Classical Limit.- 7. The Harmonic Oscillator.- 7.1. Why Study the Harmonic Oscillator?.- 7.2. Review of the Classical Oscillator.- 7.3. Quantization of the Oscillator (Coordinate Basis).- 7.4. The Oscillator in the Energy Basis.- 7.5. Passage from the Energy Basis to the X Basis.- 8. The Path Integral Formulation of Quantum Theory.- 8.1. The Path Integral Recipe.- 8.2. Analysis of the Recipe.- 8.3. An Approximation to U(t) for the Free Particle.- 8.4. Path Integral Evaluation of the Free-Particle Propagator.- 8.5. Equivalence to the Schrödinger Equation.- 8.6. Potentials of the Form V=a + bx + cx2 + d? + ex?.- 9. The Heisenberg Uncertainty Relations.- 9.1. Introduction.- 9.2. Derivation of the Uncertainty Relations.- 9.3. The Minimum Uncertainty Packet.- 9.4. Applications of the Uncertainty Principle.- 9.5. The Energy-Time Uncertainty Relation.- 10. Systems with N Degrees of Freedom.- 10.1. N Particles in One Dimension.- 10.2. More Particles in More Dimensions.- 10.3. Identical Particles.- 11. Symmetries and Their Consequences.- 11.1. Overview.- 11.2. Translational Invariance in Quantum Theory.- 11.3. Time Translational Invariance.- 11.4. Parity Invariance.- 11.5. Time-Reversal Symmetry.- 12. Rotational Invariance and Angular Momentum.- 12.1. Translations in Two Dimensions.- 12.2. Rotations in Two Dimensions.- 12.3. The Eigenvalue Problem of Lz.- 12.4. Angular Momentum in Three Dimensions.- 12.5. The Eigenvalue Problem of L2 and Lz.- 12.6. Solution of Rotationally Invariant Problems.- 13. TheHydrogen Atom.- 13.1. The Eigenvalue Problem.- 13.2. The Degeneracy of the Hydrogen Spectrum.- 13.3. Numerical Estimates and Comparison with Experiment.- 13.4. Multielectron Atoms and the Periodic Table.- 14. Spin.- 14.1. Introduction.- 14.2. What is the Nature of Spin?.- 14.3. Kinematics of Spin.- 14.4. Spin Dynamics.- 14.5. Return of Orbital Degrees of Freedom.- 15. Addition of Angular Momenta.- 15.1. A Simple Example.- 15.2. The General Problem.- 15.3. Irreducible Tensor Operators.- 15.4. Explanation of Some “Accidental” Degeneracies.- 16. Variational and WKB Methods.- 16.1. The Variational Method.- 16.2. The Wentzel-Kramers-Brillouin Method.- 17. Time-Independent Perturbation Theory.- 17.1. The Formalism.- 17.2. Some Examples.- 17.3. Degenerate Perturbation Theory.- 18. Time-Dependent Perturbation Theory.- 18.1. The Problem.- 18.2. First-Order Perturbation Theory.- 18.3. Higher Orders in Perturbation Theory.- 18.4. A General Discussion of Electromagnetic Interactions.- 18.5. Interaction of Atoms with Electromagnetic Radiation.- 19. Scattering Theory.- 19.1. Introduction.- 19.2. Recapitulation of One-Dimensional Scattering and Overview.- 19.3. The Born Approximation (Time-Dependent Description).- 19.4. Born Again (The Time-Independent Approximation).- 19.5. The Partial Wave Expansion.- 19.6. Two-Particle Scattering.- 20. The Dirac Equation.- 20.1. The Free-Particle Dirac Equation.- 20.2. Electromagnetic Interaction of the Dirac Particle.- 20.3. More on Relativistic Quantum Mechanics.- 21. Path Integrals—II.- 21.1. Derivation of the Path Integral.- 21.2. Imaginary Time Formalism.- 21.3. Spin and Fermion Path Integrals.- 21.4. Summary.- A.l. Matrix Inversion.- A.2. Gaussian Integrals.- A.3. Complex Numbers.

Recenzii

`An excellent text....The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succint manner.' - American Scientist, from a review of the First Edition

Textul de pe ultima copertă

Reviews from the First Edition:
"An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)
"No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)
Reviews of the Second Edition:
"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)
 
- Clear, accessible treatment of underlying mathematics
- A review of Newtonian, Lagrangian, and Hamiltonian mechanics
- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates
- Unsurpassed coverage of path integrals and their relevance in contemporary physics
The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Descriere

Descriere de la o altă ediție sau format:

Publish and perish-Giordano Bruno Given the number of books that already exist on the subject of quantum mechanics, one would think that the public needs one more as much as it does, say, the latest version of the Table of Integers. But this does not deter me (as it didn't my predecessors) from trying to circulate my own version of how it ought to be taught. The approach to be presented here (to be described in a moment) was first tried on a group of Harvard under­ graduates in the summer of '76, once again in the summer of '77, and more recently at Yale on undergraduates ('77-'78) and graduates ('78-'79) taking a year-long course on the subject. In all cases the results were very satisfactory in the sense that the students seemed to have learned the subject well and to have enjoyed the presentation. It is, in fact, their enthusiastic response and encouragement that convinced me of the soundness of my approach and impelled me to write this book. The basic idea is to develop the subject from its postulates, after ad­ dressing some indispensable preliminaries.