Quantum mechanics / Bruce Cameron Reed

engineering bookfair2015

Includes bibliographical references (pages 407-410) and index.

Chapter 1 Foundations -- 1.1 Faraday, Thomson, and Electrons -- 1.2 Spectra, Radiation, and Planck -- 1.3 The Rutherford-Bohr Atom -- 1.4 de Broglie Matter Waves-- Summary -- Problems -- Chapter 2 Schrödinger ’s Equation -- 2.1 The Classical Wave Equation -- 2.2 The Time-Independent Schrödinger Equation -- 2.3 The Time-Dependent Schrödinger Equation -- 2.4 Interpretation of y: Probabilities and Boundary Conditions -- Summary -- Problems -- Chapter 3 Solutions of Schrödinger ’s Equation in One Dimension -- Part I: Potential Wells -- 3.1 Concept of a Potential Well -- 3.2 The Infinite Potential Well -- 3.3 The Finite Potential Well -- 3.4 Finite Rectangular Well ¿ Even Solutions -- 3.5 Number of Bound States in a Finite Potential Well -- 3.6 Sketching Wave functions -- Part II: Potential Barriers and Scattering -- 3.7 Potential Barriers -- 3.8 Penetration of Arbitrarily-Shaped Barriers -- 3.9 Alpha-Decay as a Barrier Penetration Effect -- 3.10 Scattering by One-Dimensional Potential Wells -- Summary -- Problems -- Chapter 4 Operators, Expectation Values, and the Uncertainty Principle -- 4.1 Properties of Operators -- 4.2 Expectation Values -- 4.3 The Uncertainty Principle -- 4.4 Commutators and Uncertainty Relations -- 4.5 Ehrenfest ’s Theorem -- 4.6 The Orthogonality Theorem -- 4.7 The Superposition Theorem -- 4.8 Constructing a Time-Dependent Wave Packet -- 4.9 The Viral Theorem -- Summary -- Problems-- Chapter 5 The Harmonic Oscillator -- 5.1 A Lesson in Dimensional Analysis -- 5.2 The Asymptotic Solution -- 5.3 The Series Solution -- 5.4 Hermite Polynomials and Harmonic Oscillator Wave functions -- 5.5 Comparing the Classical and Quantum Simple Harmonic Oscillators -- 5.6 Raising and Lowering Operators (Optional) -- Summary -- Problems -- Chapter 6 The Schrödinger Equation in Three Dimensions and an Introduction to the Quantum Theory of Angular Momentum -- 6.1 Separation of Variables ¿ Cartesian Coordinates -- 6.2 Spherical Coordinates -- 6.3 Angular Momentum Operators -- 6.4 Separation of Variables in Spherical Coordinates: Central Potentials -- 6.5 Angular Wavefunctions and Spherical Harmonics -- 6.5.1 Solution of the F Equation -- 6.5.2 Solution of the Q Equation -- 6.5.3 Spherical Harmonics -- Summary -- Problems -- Chapter 7 Central Potentials -- 7.1 Introduction -- 7.2 The Infinite Spherical Well -- 7.3 The Finite Spherical Well -- 7.4 The Coulomb Potential -- 7.5 Hydrogen Atom Probability Distributions -- 7.5.1 The (1,0,0) State of hydrogen -- 7.5.2 The (2,0,0) and other States of hydrogen -- 7.6 The Effective Potential -- 7.7 Some Philosophical Remarks -- Summary -- Problems -- Chapter 8 Further Developments with Angular Momentum and Multi-Particle Systems -- 8.1 Angular Momentum Raising and Lowering Operators -- 8.2 The Stern-Gerlach Experiment: Evidence for Quantized Angular Momentum and Electron Spin -- 8.3 Diatomic Molecules and Angular Momentum -- 8.4 Identical Particles, Indistinguishability, and the Pauli Exclusion Principle -- Chapter 9 Approximation Methods -- 9.1 The WKB Method -- 9.2 The Superposition Theorem Revisited -- 9.3 Perturbation Theory -- 9.4 The Variational Method -- 9.5 Improving the Variational Method (Optional) -- Summary -- Problems -- Chapter 10 Numerical Solution of the Schrödinger Equation -- 10.1 Atomic Units -- 10.2 A Straightforward Numerical Integration Method -- Summary -- Problems -- Chapter 11 A Sampling of Results from Time-Dependent Quantum Mechanics:Transition Rates and Probabilities -- 11.1 Transition Frequencies -- 11.2 Transition Rules -- 11.3 The Sudden Approximation -- Summary -- Problems -- Appendix A Miscellaneous Derivations -- A1 Heisenberg’s Uncertainty Principle -- A2 Explicit series form for Associated Legendre Functions -- A3 Proof that -- A4 Radial nodes in hydrogen wavefunctions -- Appendix B Answers to Selected Problems -- Appendix C Integrals and Trigonometric Identities -- Appendix D Physical Constants