Quantum Mechanics : Classical Results, Modern Systems, and Visualized Examples.

By: Robinett, RichardPublisher: Oxford : Oxford University Press USA - OSO, 2006Copyright date: ©2006Edition: 2nd edDescription: 1 online resource (722 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780191523984Subject(s): Quantum theoryGenre/Form: Electronic books. Additional physical formats: Print version:: Quantum Mechanics : Classical Results, Modern Systems, and Visualized ExamplesDDC classification: 530.12 LOC classification: QC174.12.R6 2006Online resources: Click to View
Contents:
Intro -- CONTENTS -- Part I: The Quantum Paradigm -- 1 A First Look at Quantum Physics -- 1.1 How this Book Approaches Quantum Mechanics -- 1.2 Essential Relativity -- 1.3 Quantum Physics: h as a Fundamental Constant -- 1.4 Semiclassical Model of the Hydrogen Atom -- 1.5 Dimensional Analysis -- 1.6 Questions and Problems -- 2 Classical Waves -- 2.1 The Classical Wave Equation -- 2.2 Wave Packets and Periodic Solutions -- 2.3 Fourier Transforms -- 2.4 Inverting the Fourier transform: the Dirac δ-function -- 2.5 Dispersion and Tunneling -- 2.6 Questions and Problems -- 3 The Schrödinger Wave Equation -- 3.1 The Schrödinger Equation -- 3.2 Plane Waves and Wave Packet Solutions -- 3.3 "Bouncing" Wave Packets -- 3.4 Numerical Calculation of Wave Packets -- 3.5 Questions and Problems -- 4 Interpreting the Schrödinger Equation -- 4.1 Introduction to Probability -- 4.2 Probability Interpretation of the Schrödinger Wavefunction -- 4.3 Average Values -- 4.4 Real Average Values and Hermitian Operators -- 4.5 The Physical Interpretation of φ(p) -- 4.6 Energy Eigenstates, Stationary States, and the Hamiltonian Operator -- 4.7 The Schrödinger Equation in Momentum Space -- 4.8 Commutators -- 4.9 The Wigner Quasi-Probability Distribution -- 4.10 Questions and Problems -- 5 The Infinite Well: Physical Aspects -- 5.1 The Infinite Well in Classical Mechanics: Classical Probability Distributions -- 5.2 Stationary States for the Infinite Well -- 5.3 The Asymmetric Infinite Well -- 5.4 Time-Dependence of General Solutions -- 5.5 Questions and Problems -- 6 The Infinite Well: Formal Aspects -- 6.1 Dirac Bracket Notation -- 6.2 Eigenvalues of Hermitian Operators -- 6.3 Orthogonality of Energy Eigenfunctions -- 6.4 Expansions in Eigenstates -- 6.5 Expansion Postulate and Time-Dependence -- 6.6 Parity -- 6.7 Simultaneous Eigenfunctions -- 6.8 Questions and Problems.
7 Many Particles in the Infinite Well: The Role of Spin and Indistinguishability -- 7.1 The Exclusion Principle -- 7.2 One-Dimensional Systems -- 7.3 Three-Dimensional Infinite Well -- 7.4 Applications -- 7.5 Questions and Problems -- 8 Other One-Dimensional Potentials -- 8.1 Singular Potentials -- 8.2 The Finite Well -- 8.3 Applications to Three-Dimensional Problems -- 8.4 Questions and Problems -- 9 The Harmonic Oscillator -- 9.1 The Importance of the Simple Harmonic Oscillator -- 9.2 Solutions for the SHO -- 9.3 Experimental Realizations of the SHO -- 9.4 Classical Limits and Probability Distributions -- 9.5 Unstable Equilibrium: Classical and Quantum Distributions -- 9.6 Questions and Problems -- 10 Alternative Methods of Solution and Approximation Methods -- 10.1 Numerical Integration -- 10.2 The Variational or Rayleigh-Ritz Method -- 10.3 The WKB method -- 10.4 Matrix Methods -- 10.5 Perturbation Theory -- 10.6 Questions and Problems -- 11 Scattering -- 11.1 Scattering in One-Dimensional Systems -- 11.2 Scattering from a Step Potential -- 11.3 Scattering from the Finite Square Well -- 11.4 Applications of Quantum Tunneling -- 11.5 Questions and Problems -- 12 More Formal Topics -- 12.1 Hermitian Operators -- 12.2 Quantum Mechanics, Linear Algebra, and Vector Spaces -- 12.3 Commutators -- 12.4 Uncertainty Principles -- 12.5 Time-Dependence and Conservation Laws in Quantum Mechanics -- 12.6 Propagators -- 12.7 Timescales in Bound State Systems: Classical Period and Quantum Revival Times -- 12.8 Questions and Problems -- 13 Operator and Factorization Methods for the Schrödinger Equation -- 13.1 Factorization Methods -- 13.2 Factorization of the Harmonic Oscillator -- 13.3 Creation and Annihilation Operators -- 13.4 Questions and Problems -- 14 Multiparticle Systems -- 14.1 Generalities -- 14.2 Separable Systems -- 14.3 Two-Body Systems.
14.4 Spin Wavefunctions -- 14.5 Indistinguishable Particles -- 14.6 Questions and Problems -- Part II: The Quantum World -- 15 Two-Dimensional Quantum Mechanics -- 15.1 2D Cartesian Systems -- 15.2 Central Forces and Angular Momentum -- 15.3 Quantum Systems with Circular Symmetry -- 15.4 Questions and Problems -- 16 The Schrödinger Equation in Three Dimensions -- 16.1 Spherical Coordinates and Angular Momentum -- 16.2 Eigenfunctions of Angular Momentum -- 16.3 Diatomic Molecules -- 16.4 Spin and Angular Momentum -- 16.5 Addition of Angular Momentum -- 16.6 Free Particle in Spherical Coordinates -- 16.7 Questions and Problems -- 17 The Hydrogen Atom -- 17.1 Hydrogen Atom Wavefunctions and Energies -- 17.2 The Classical Limit of the Quantum Kepler Problem -- 17.3 Other "Hydrogenic" Atoms -- 17.4 Multielectron Atoms -- 17.5 Questions and Problems -- 18 Gravity and Electromagnetism in Quantum Mechanics -- 18.1 Classical Gravity and Quantum Mechanics -- 18.2 Electromagnetic Fields -- 18.3 Constant Electric Fields -- 18.4 Atoms in Electric Fields: The Stark Effect -- 18.5 Constant Magnetic Fields -- 18.6 Atoms in Magnetic Fields -- 18.7 Spins in Magnetic Fields -- 18.8 The Aharonov-Bohm Effect -- 18.9 Questions and Problems -- 19 Scattering in Three Dimensions -- 19.1 Classical Trajectories and Cross-Sections -- 19.2 Quantum Scattering -- 19.3 Electromagnetic Scattering -- 19.4 Partial Wave Expansions -- 19.5 Scattering of Particles -- 19.6 Questions and Problems -- A: Dimensions and MKS-type Units for Mechanics, Electricity and Magnetism, and Thermal Physics -- A.1 Problems -- B: Physical Constants, Gaussian Integrals, and the Greek Alphabet -- B.1 Physical Constants -- B.2 The Greek Alphabet -- B.3 Gaussian Probability Distribution -- B.4 Problems -- C: Complex Numbers and Functions -- C.1 Problems -- D: Integrals, Summations, and Calculus Results.
D.1 Integrals -- D.2 Summations and Series Expansions -- D.3 Assorted Calculus Results -- D.4 Real Integrals by Contour Integration -- D.5 Plotting -- D.6 Problems -- E: Special Functions -- E.1 Trigonometric and Exponential Functions -- E.2 Airy Functions -- E.3 Hermite Polynomials -- E.4 Cylindrical Bessel Functions -- E.5 Spherical Bessel Functions -- E.6 Legendre Polynomials -- E.7 Generalized Laguerre Polynomials -- E.8 The Dirac δ-Function -- E.9 The Euler Gamma Function -- E.10 Problems -- F: Vectors, Matrices, and Group Theory -- F.1 Vectors and Matrices -- F.2 Group Theory -- F.3 Problems -- G: Hamiltonian Formulation of Classical Mechanics -- G.1 Problems -- REFERENCES -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.
Summary: `Quantum Mechanics' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena.
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Intro -- CONTENTS -- Part I: The Quantum Paradigm -- 1 A First Look at Quantum Physics -- 1.1 How this Book Approaches Quantum Mechanics -- 1.2 Essential Relativity -- 1.3 Quantum Physics: h as a Fundamental Constant -- 1.4 Semiclassical Model of the Hydrogen Atom -- 1.5 Dimensional Analysis -- 1.6 Questions and Problems -- 2 Classical Waves -- 2.1 The Classical Wave Equation -- 2.2 Wave Packets and Periodic Solutions -- 2.3 Fourier Transforms -- 2.4 Inverting the Fourier transform: the Dirac δ-function -- 2.5 Dispersion and Tunneling -- 2.6 Questions and Problems -- 3 The Schrödinger Wave Equation -- 3.1 The Schrödinger Equation -- 3.2 Plane Waves and Wave Packet Solutions -- 3.3 "Bouncing" Wave Packets -- 3.4 Numerical Calculation of Wave Packets -- 3.5 Questions and Problems -- 4 Interpreting the Schrödinger Equation -- 4.1 Introduction to Probability -- 4.2 Probability Interpretation of the Schrödinger Wavefunction -- 4.3 Average Values -- 4.4 Real Average Values and Hermitian Operators -- 4.5 The Physical Interpretation of φ(p) -- 4.6 Energy Eigenstates, Stationary States, and the Hamiltonian Operator -- 4.7 The Schrödinger Equation in Momentum Space -- 4.8 Commutators -- 4.9 The Wigner Quasi-Probability Distribution -- 4.10 Questions and Problems -- 5 The Infinite Well: Physical Aspects -- 5.1 The Infinite Well in Classical Mechanics: Classical Probability Distributions -- 5.2 Stationary States for the Infinite Well -- 5.3 The Asymmetric Infinite Well -- 5.4 Time-Dependence of General Solutions -- 5.5 Questions and Problems -- 6 The Infinite Well: Formal Aspects -- 6.1 Dirac Bracket Notation -- 6.2 Eigenvalues of Hermitian Operators -- 6.3 Orthogonality of Energy Eigenfunctions -- 6.4 Expansions in Eigenstates -- 6.5 Expansion Postulate and Time-Dependence -- 6.6 Parity -- 6.7 Simultaneous Eigenfunctions -- 6.8 Questions and Problems.

7 Many Particles in the Infinite Well: The Role of Spin and Indistinguishability -- 7.1 The Exclusion Principle -- 7.2 One-Dimensional Systems -- 7.3 Three-Dimensional Infinite Well -- 7.4 Applications -- 7.5 Questions and Problems -- 8 Other One-Dimensional Potentials -- 8.1 Singular Potentials -- 8.2 The Finite Well -- 8.3 Applications to Three-Dimensional Problems -- 8.4 Questions and Problems -- 9 The Harmonic Oscillator -- 9.1 The Importance of the Simple Harmonic Oscillator -- 9.2 Solutions for the SHO -- 9.3 Experimental Realizations of the SHO -- 9.4 Classical Limits and Probability Distributions -- 9.5 Unstable Equilibrium: Classical and Quantum Distributions -- 9.6 Questions and Problems -- 10 Alternative Methods of Solution and Approximation Methods -- 10.1 Numerical Integration -- 10.2 The Variational or Rayleigh-Ritz Method -- 10.3 The WKB method -- 10.4 Matrix Methods -- 10.5 Perturbation Theory -- 10.6 Questions and Problems -- 11 Scattering -- 11.1 Scattering in One-Dimensional Systems -- 11.2 Scattering from a Step Potential -- 11.3 Scattering from the Finite Square Well -- 11.4 Applications of Quantum Tunneling -- 11.5 Questions and Problems -- 12 More Formal Topics -- 12.1 Hermitian Operators -- 12.2 Quantum Mechanics, Linear Algebra, and Vector Spaces -- 12.3 Commutators -- 12.4 Uncertainty Principles -- 12.5 Time-Dependence and Conservation Laws in Quantum Mechanics -- 12.6 Propagators -- 12.7 Timescales in Bound State Systems: Classical Period and Quantum Revival Times -- 12.8 Questions and Problems -- 13 Operator and Factorization Methods for the Schrödinger Equation -- 13.1 Factorization Methods -- 13.2 Factorization of the Harmonic Oscillator -- 13.3 Creation and Annihilation Operators -- 13.4 Questions and Problems -- 14 Multiparticle Systems -- 14.1 Generalities -- 14.2 Separable Systems -- 14.3 Two-Body Systems.

14.4 Spin Wavefunctions -- 14.5 Indistinguishable Particles -- 14.6 Questions and Problems -- Part II: The Quantum World -- 15 Two-Dimensional Quantum Mechanics -- 15.1 2D Cartesian Systems -- 15.2 Central Forces and Angular Momentum -- 15.3 Quantum Systems with Circular Symmetry -- 15.4 Questions and Problems -- 16 The Schrödinger Equation in Three Dimensions -- 16.1 Spherical Coordinates and Angular Momentum -- 16.2 Eigenfunctions of Angular Momentum -- 16.3 Diatomic Molecules -- 16.4 Spin and Angular Momentum -- 16.5 Addition of Angular Momentum -- 16.6 Free Particle in Spherical Coordinates -- 16.7 Questions and Problems -- 17 The Hydrogen Atom -- 17.1 Hydrogen Atom Wavefunctions and Energies -- 17.2 The Classical Limit of the Quantum Kepler Problem -- 17.3 Other "Hydrogenic" Atoms -- 17.4 Multielectron Atoms -- 17.5 Questions and Problems -- 18 Gravity and Electromagnetism in Quantum Mechanics -- 18.1 Classical Gravity and Quantum Mechanics -- 18.2 Electromagnetic Fields -- 18.3 Constant Electric Fields -- 18.4 Atoms in Electric Fields: The Stark Effect -- 18.5 Constant Magnetic Fields -- 18.6 Atoms in Magnetic Fields -- 18.7 Spins in Magnetic Fields -- 18.8 The Aharonov-Bohm Effect -- 18.9 Questions and Problems -- 19 Scattering in Three Dimensions -- 19.1 Classical Trajectories and Cross-Sections -- 19.2 Quantum Scattering -- 19.3 Electromagnetic Scattering -- 19.4 Partial Wave Expansions -- 19.5 Scattering of Particles -- 19.6 Questions and Problems -- A: Dimensions and MKS-type Units for Mechanics, Electricity and Magnetism, and Thermal Physics -- A.1 Problems -- B: Physical Constants, Gaussian Integrals, and the Greek Alphabet -- B.1 Physical Constants -- B.2 The Greek Alphabet -- B.3 Gaussian Probability Distribution -- B.4 Problems -- C: Complex Numbers and Functions -- C.1 Problems -- D: Integrals, Summations, and Calculus Results.

D.1 Integrals -- D.2 Summations and Series Expansions -- D.3 Assorted Calculus Results -- D.4 Real Integrals by Contour Integration -- D.5 Plotting -- D.6 Problems -- E: Special Functions -- E.1 Trigonometric and Exponential Functions -- E.2 Airy Functions -- E.3 Hermite Polynomials -- E.4 Cylindrical Bessel Functions -- E.5 Spherical Bessel Functions -- E.6 Legendre Polynomials -- E.7 Generalized Laguerre Polynomials -- E.8 The Dirac δ-Function -- E.9 The Euler Gamma Function -- E.10 Problems -- F: Vectors, Matrices, and Group Theory -- F.1 Vectors and Matrices -- F.2 Group Theory -- F.3 Problems -- G: Hamiltonian Formulation of Classical Mechanics -- G.1 Problems -- REFERENCES -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.

`Quantum Mechanics' is a comprehensive introduction to quantum mechanics for advanced undergraduate students in physics. It provides the reader with a strong conceptual background in the subject, extensive experience with the necessary mathematical background, as well as numerous visualizations of quantum concepts and phenomena.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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