Quantum mechanics : an enhanced primer / / Bruce Cameron Reed

• Autore: Reed Bruce Cameron
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (407 pages)
• Disciplina: 530.12
• Soggetto topico: Quantum theory
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- About the Author -- 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 -- 1.5 The Radiative Collapse Problem (Optional) -- References -- 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 ψ: Probabilities and Boundary Conditions -- References -- 3 Solutions of Schrödinger's Equation in One Dimension -- 3.1 Concept of a Potential Well -- 3.2 The Infinite Potential Well -- 3.3 The Finite Potential Well -- 3.3.1 A Matrix Approach to the Finite Potential Well -- 3.4 Finite Potential Well-Even Solutions -- 3.5 Number of Bound States in a Finite Potential Well -- 3.6 Sketching Wavefunctions -- 3.7 Potential Barriers and Scattering -- 3.8 Penetration of Arbitrarily-Shaped Barriers -- 3.9 Alpha-Decay as a Barrier Penetration Effect -- 3.10 Scattering by One-Dimensional Potential Wells -- References -- 4 Operators, Expectation Values, and Various Quantum Theories -- 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 Virial Theorem -- 4.10 Momentum-Space Wavefunctions -- References -- 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 Wavefunctions -- 5.5 Comparing the Classical and Quantum Harmonic Oscillators -- 5.6 Raising and Lowering Operators -- Reference. ; 6 Schrödinger's Equation in Three Dimensions and 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 Φ Equation -- 6.5.2 Solution of the Θ Equation -- 6.5.3 Spherical Harmonics -- References -- 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 -- References -- 8 Further Developments with Angular Momentum and Multiparticle Systems -- 8.1 Angular Momentum Raising and Lowering Operators -- 8.2 The Stern-Gerlach Experiment: Evidence for Qunatized Angular … -- 8.3 Diatomic Molecules and Angular Momentum -- 8.4 Identical Particles, Indistinguishability, and the Pauli Exclusion Principle -- References -- 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 -- References -- 10 Numerical Solution of Schrödinger's Equation -- 10.1 Atomic Units -- 10.2 A Straightforward Numerical Integration Method -- References -- 11 A Few Results from Time-Dependent Quantum Mechanics: Transition Rates and Probabilities -- 11.1 Transition Frequencies -- 11.2 Transition Rules -- 11.3 The Sudden Approximation -- References -- Appendix A Miscellaneous Derivations -- A.1 Heisenberg's Uncertainty Principle -- A.2 Normalization of Hermite Polynomials. ; A.3 Explicit Series Form for Associated Legendre Functions -- A.4 Proof That upper Y Subscript script l comma negative m Baseline equals left parenthesis negative 1 right parenthesis Superscript m Baseline upper Y Subscript script l comma m Superscript asteriskYell,-m = (-1)mYell,m* -- A.5 Radial Nodes in Hydrogen Wavefunctions -- Appendix B Answers to Selected Odd-Numbered Problems -- Appendix C Integrals and Trigonometric Identities -- Appendix D Physical Constants -- Index.
• Titolo autorizzato: Quantum Mechanics
• ISBN: 9783031140204; 9783031140198
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910633920803321
• Lo trovi qui: Univ. Federico II