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)
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.

lgrsnf/1994_Book_PrinciplesOfQuantumMechanics.pdf

nexusstc/Principles of Quantum Mechanics/eeb10c98c8b91ec53b84c219723b58a1.pdf

scihub/10.1007/978-1-4757-0576-8.pdf

Basic training in mathematics : a fitness program for science students

Shankar, Ramamutri

Ramamurti Shankar

Springer US : Imprint : Springer

Da Capo Press, Incorporated

Hachette Books

Hachette GO

Springer Nature (Textbooks & Major Reference Works), Boston, MA, 1994

2nd ed., New York, New York State, 1994

2. ed., New York; London, Unknown, 1994

United States, United States of America

2nd ed. 1994, New York, NY, 1994

2nd, Second Edition, US, 2005

New York, ©1995

Jul 08, 2012

lg2867038

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Includes bibliographical references and index.

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Preface to the Second Edition
Preface to the First Edition
For Whom Is this Book Intended?
Acknowledgments
Prelude
Note to the Student
Contents
1 Mathematical Introduction
1.1. Linear Vector Spaces: Basics
1.2. Inner Product Spaces
1.3. Dual Spaces and the Dirac Notation
1.3.1. Expansion of Vectors in an Orthonormal Basis
1.3.2. Adjoint Operation
Gram-Schmidt Theorem
Schwarz and Triangle Inequalities
1.4. Subspaces
1.5. Linear Operators
1.6. Matrix Elements of Linear Operators
Matrices Corresponding to Products of Operators
The Adjoint of an Operator
Hermitian, Anti-Hermitian, and Unitary Operators
1. 7. Active and Passive Transformations
1.8. The Eigenvalue Problem
The Characteristic Equation and the Solution to the Eigenvalue Problem
Degeneracy
Diagonalization of Hermitian Matrices
Simultaneous Diagonalization of Two Hermitian Operators
The Normal Modes
1.9. Functions of Operators and Related Concepts
Derivatives of Operators with Respect to Parameters
1.10. Generalization to Infinite Dimensions
Operators in 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
Canonical Transformations
Active Transformations
2.8. Symmetries and Their Consequences
A Useful Relation Between SandE
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 Postulatest
4.2. Discussion of Postulates I-III
CoUapse of the State Vector
How to Test Quantum Theory
Expectation Value
The Uncertainty
Compatible and Incompatible Variables
The Density Matrix-a Digressiont
Generalization to More Degrees of Freedom
4.3. The Schrodinger Equation (Dotting Your i 's and Crossing Your h's)
Setting Up the Schrödinger Equation
General Approach to the Solution
Choosing a Basis for Solving Schrodinger's Equation
5 Simple Problems in
One Dimension
5.1. The Free Particle
Time Evolution of the Gaussian Packet
Some General Features of Energy Eigenfunctions
5.2. The Particle in a Box
5.3. The Continuity Equation for Probability
Ensemble Interpretation of j
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 OscUla tor
7.3. Quantization of the Oscillator (Coordinate Basis)
7 .4. The OsciUator 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 a Free Particle
8.4. Path Integral Evaluation of the Free-Particle Propagator
8.5. Equivalence to the Schrodinger Equation
8.6. Potentials of the Form V =a + bx + cx2 + di +exx
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
The Two-Particle Hilbert Space
V 102 As a Direct Product Space
The Direct Product Revisited
Evolution of the Two-Particle State Vector
N Particles in One Dimension
10.2. More Particles in More Dimensions
10.3. Identical Particles
The Classical Case
Two-Particle Systems-Symmetric and Antisymmetric States
Bosons and Fermions
Bosonic and Fermionic Hilbert Spaces
Determination of Particle Statistics
Systems of N Identical Particles
When Can We Ignore Symmetrization and Antisymmetrization?
11 Symmetries and
Their Consequences
11.1. Overview
11.2. Translational Invariance in Quantum Theory
Translation in Terms of Passive Transformations
A Digression on the Analogy with Classical Mechanicst
Finite Translations
A Digression on Finite Canonical and Unitary Transformations
System of Particles
Implications of Translational Invariances
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
Explicit Construction of U[R]
12.3. The Eigenvalue Problem of Lz
Solutions to Rotationally Invariant Problems
12.4. Angular Momentum in Three Dimensions
12.5. The Eigenvalue Problem of L 2 and Lz
Finite Rotations
Angular Momentum Eigenfunctions in the Coordinate Basis
12.6. Solution of Rotationally Invariant Problems
General Properties of U Et
The Free Particle in Spherical Coordinates
Connection with the Solution in Cartesian Coordinates
The Isotropic Oscillator
13 The Hydrogen Atom
13.1. The Eigenvalue Problem
The Energy Levels
The Wave Functions
13.2. The Degeneracy of the Hydrogen Spectrum
13.3. Numerical Estimates and Comparison with Experiment
Numerical Estimates
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
Explicit Forms of Rotation Operators
14.4. Spin Dynamics
Orbital Magnetic Moment in Quantum Theory
Spin Magnetic Moment
Paramagnetic Resonance
Negative Absolute Temperature (Optional Digression)
14.5. Return of Orbital Degrees of Freedom
The Stern-Gerlach (SG) Experiment
15 Addition of Angular Momenta
15.1. A Simple Example
15.2. The General Problem
Clebsch-Gordan (CG) Coefficients
Addition of L and S
The Modified Spectroscopic Notation
15.3. Irreducible Tensor Operators
Tensor Operators
15.4. Explanation of Some "Accidental" Degeneracies
Hydrogen
The Oscillator
The Free-Particle Solutions
16 The Variational and WKB Methods
16.1. The Variational Method
16.2. The Wentzel-Kramers--Brillouin Method
Connection with the Path Integral Formalism
Tunneling Amplitudes
Bound States
17 Time-Independent Perturbation Theory
17.1. The Formalism
17.2. Some Examples
Selection Rules
17.3. Degenerate Perturbation Theory
Fine Structure
18 Time-Dependent Perturbation Theory
18.1. The Problem
18.2. First-Order Perturbation Theory
The Sudden Perturbation
The Adiabatic Perturbation
The Periodic Perturbation
18.3. Higher Orders in Perturbation Theory
The Interaction Picture
The Heisenberg Picture
18.4. A General Discussion of Electromagnetic Interactions
Classical Electrodynamics
The Potentials in Quantum Theory
18.5. Interaction of Atoms with Electromagnetic Radiation
Photoelectric Effect in Hydrogen
Field Quantization
Spontaneous Decay
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 Description)
Validity of the Born Approximation
19.5. The Partial Wave Expansion
A Model Calculation of δ1: The Hard Sphere
Resonances
19.6. Two-Particle Scattering
Passage to the Lab Frame
Scattering of Identical Particles
20 The Dirac Equation
20.1. The Free-Particle Dirac Equation
20.2. Electromagnetic Interaction of the Dirac Particle
The Electron Spin and Magnetic Moment
Hydrogen Fine Structure
20.3. More on Relativistic Quantum Mechanics
21 Path Integrals: Part II
21.1. Derivation of the Path Integral
The Landau Levels
The Berry Phase
Coherent State Path Integral
21.2. Imaginary Time Formalism
Path Integral for the Imaginary Time Propagator
Tunneling by Path Integrals: Well, well!
Spontaneous Symmetry Breaking
Imaginary Time Path Integrals and Quantum Statistical Mechanics
Relation to Classical Statistical Mechanics
21.3. Spin and Fermion Path Integrals
Spin Coherent States and Path Integral
Fermion Oscillator and Coherent States
The Fermionic Path Integral
21.4. Summary
Bibliography
Appendix
A.1. Matrix Inversion
A.2. Gaussian Integrals
A.3. Complex Numbers
A.4. The iε Prescription
Answers to Selected Exercises
Table of Constants
Index

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 physicsThe requisite text for advanced undergraduate-level 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.

A textbook on quantum mechanics that develops the subject from its postulates, beginning with a rather lengthy chapter in which the relevant mathematics of vector spaces is developed from simple ideas on vectors and matrices students are assumed to know. This revised edition (1st ed., 1980) adds a discussion of time-reversal invariance and a new chapter, Path Integrals: Part II, which discusses many kinds of path integrals and their uses. Annotation copyright by Book News, Inc., Portland, OR

2020-11-29