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El. knyga: Quantum Mechanics: An Enhanced Primer

  • Formatas: EPUB+DRM
  • Išleidimo metai: 30-Nov-2022
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783031140204
Kitos knygos pagal šią temą:
Quantum Mechanics: An Enhanced PrimerDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 30-Nov-2022
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783031140204
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Quantum mechanics is one of the most fascinating elements of the physics curriculum, but its conceptual nuances and mathematical complexity can be daunting for beginning students. This user-friendly text is designed for a one-semester course which bridges the gap between sophomore-level treatments and advanced undergraduate/lower-graduate courses. Qualitative explanations and descriptions of historical background are combined with detailed mathematical analyses to help students establish a firm foundation for further study. Classical problems such potential wells, barrier penetration, alpha decay, the harmonic oscillator, and the hydrogen atom are examined in detail, and formalisms and techniques such as operators, expectation values, commutators, perturbation theory, numerical solutions, and the variational theorem are also covered. Particular emphasis is placed on providing numerous worked examples and exercises.
1 Foundations
1(34)
1.1 Faraday, Thomson, and Electrons
2(2)
1.2 Spectra, Radiation, and Planck
4(8)
1.3 The Rutherford-Bohr Atom
12(8)
1.4 De Broglie Matter Waves
20(4)
1.5 The Radiative Collapse Problem (Optional)
24(11)
References
32(3)
2 Schrodinger's Equation
35(22)
2.1 The Classical Wave Equation
36(5)
2.2 The Time-Independent Schrodinger Equation
41(3)
2.3 The Time-Dependent Schrodinger Equation
44(5)
2.4 Interpretation of Ψ: Probabilities and Boundary Conditions
49(8)
References
56(1)
3 Solutions of Schrodinger's Equation in One Dimension
57(54)
3.1 Concept of a Potential Well
58(2)
3.2 The Infinite Potential Well
60(7)
3.3 The Finite Potential Well
67(11)
3.3.1 A Matrix Approach to the Finite Potential Well
75(3)
3.4 Finite Potential Well-Even Solutions
78(2)
3.5 Number of Bound States in a Finite Potential Well
80(3)
3.6 Sketching Wavefunctions
83(4)
3.7 Potential Barriers and Scattering
87(5)
3.8 Penetration of Arbitrarily-Shaped Barriers
92(2)
3.9 Alpha-Decay as a Barrier Penetration Effect
94(6)
3.10 Scattering by One-Dimensional Potential Wells
100(11)
References
109(2)
4 Operators, Expectation Values, and Various Quantum Theories
111(46)
4.1 Properties of Operators
112(3)
4.2 Expectation Values
115(8)
4.3 The Uncertainty Principle
123(4)
4.4 Commutators and Uncertainty Relations
127(3)
4.5 Ehrenfest's Theorem
130(2)
4.6 The Orthogonality Theorem
132(2)
4.7 The Superposition Theorem
134(2)
4.8 Constructing a Time-Dependent Wave Packet
136(5)
4.9 The Virial Theorem
141(6)
4.10 Momentum-Space Wavefunctions
147(10)
References
156(1)
5 The Harmonic Oscillator
157(30)
5.1 A Lesson in Dimensional Analysis
158(3)
5.2 The Asymptotic Solution
161(2)
5.3 The Series Solution
163(7)
5.4 Hermite Polynomials and Harmonic Oscillator Wavefunctions
170(3)
5.5 Comparing the Classical and Quantum Harmonic Oscillators
173(3)
5.6 Raising and Lowering Operators
176(11)
Reference
186(1)
6 Schrodinger's Equation in Three Dimensions and the Quantum Theory of Angular Momentum
187(38)
6.1 Separation of Variables: Cartesian Coordinates
188(7)
6.2 Spherical Coordinates
195(2)
6.3 Angular Momentum Operators
197(6)
6.4 Separation of Variables in Spherical Coordinates: Central Potentials
203(2)
6.5 Angular Wavefunctions and Spherical Harmonics
205(20)
6.5.1 Solution of the Φ Equation
206(2)
6.5.2 Solution of the Equation
208(5)
6.5.3 Spherical Harmonics
213(10)
References
223(2)
7 Central Potentials
225(40)
7.1 Introduction
225(3)
7.2 The Infinite Spherical Well
228(2)
7.3 The Finite Spherical Well
230(3)
7.4 The Coulomb Potential
233(12)
7.5 Hydrogen Atom Probability Distributions
245(11)
7.5.1 The (1, 0, 0) State of Hydrogen
246(3)
7.5.2 The (2, 0, 0) and Other States of Hydrogen
249(7)
7.6 The Effective Potential
256(1)
7.7 Some Philosophical Remarks
257(8)
References
264(1)
8 Further Developments with Angular Momentum and Multiparticle Systems
265(22)
8.1 Angular Momentum Raising and Lowering Operators
265(7)
8.2 The Stern-Gerlach Experiment: Evidence for Qunatized Angular Momentum and Electron Spin
272(4)
8.3 Diatomic Molecules and Angular Momentum
276(4)
8.4 Identical Particles, Indistinguishability, and the Pauli Exclusion Principle
280(7)
References
285(2)
9 Approximation Methods
287(46)
9.1 The WKB Method
288(5)
9.2 The Superposition Theorem Revisited
293(3)
9.3 Perturbation Theory
296(17)
9.4 The Variational Method
313(8)
9.5 Improving the Variational Method
321(12)
References
332(1)
10 Numerical Solution of Schrodinger's Equation
333(16)
10.1 Atomic Units
334(1)
10.2 A Straightforward Numerical Integration Method
335(14)
References
348(1)
11 A Few Results from Time-Dependent Quantum Mechanics: Transition Rates and Probabilities
349(8)
11.1 Transition Frequencies
350(2)
11.2 Transition Rules
352(1)
11.3 The Sudden Approximation
353(4)
References
356(1)
Appendix A Miscellaneous Derivations 357(24)
Appendix B Answers to Selected Odd-Numbered Problems 381(4)
Appendix C Integrals and Trigonometric Identities 385(4)
Appendix D Physical Constants 389(2)
Index 391
Bruce Cameron Reed earned a Ph.D. from the University of Waterloo (Canada) in 1984. His doctoral work was in observational astronomy, a study of the distribution of stars in the Puppis direction of the Milky Way. Just before formally finishing his graduate work, he became a faculty member in the Department of Physics at Saint Marys University in Halifax, Nova Scotia, in 1983. There he continued to work in observational astronomy, and, in 1992, took up a position as Associate Professor of Physics at Alma College in Michigan. At Alma he began to develop an interest in the history and physics of the Manhattan Project. This grew into his primary research focus, and has resulted in several dozen journal papers, five books (three with Springer, one of which has gone into a third edition), and the teaching of a general-education class on the development of nuclear weapons. Prof. Reed was elected a Fellow of the American Physical Society (APS) in 2009 in recognition of hiswork on the Manhattan Project, served as Editor of the APSs Physics & Society newsletter (2009-13), and as Secretary-Treasurer of the Societys Forum on History of Physics (2013-19).

In 2010 Prof. Reed was appointed one of six Charles A. Dana Professors at Alma, and in 2017 named an Alumni of Honour at Waterloo. He formally retired at the end of 2017 and returned to the Halifax area, where he continues to teach part-time, serves as an Associate Editor with the American Journal of Physics, and does occasional consulting work.
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