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Description: Quantum mechanics and its applications are a vibrant, central part of today’s research in both experimental and theoretical physics. Designed for the one-semester course, Quantum Mechanics expertly guides students through rigorous course material, providing comprehensive explanations, accessible examples, and intuitive equations. This text’s in-depth coverage of essential topics, such as the harmonic oscillator, barrier penetration, and hydrogen atoms, skillfully bridges the gap between sophomore introductory texts and lower-level graduate treatments. Students will find that this user-friendly text, with numerous examples and applications, sets a solid foundation for future courses in quantum mechanics.
Key features:
• Covers the basics of time-independent one- and three-dimensional quantum mechanics (Schrödinger’s equation, potential wells, barrier penetration, the harmonic oscillator, separation of variables, degeneracy, etc.) in a package that can be covered in one semester.
• Each chapter begins with an introduction that summarizes key points, discussing how new material builds upon topics presented in previous chapters, how its topics fit into the larger picture of quantum mechanics, and why the topic is considered important in that larger picture.
• Key points are summarized at the end of each chapter, and numerous end-of-chapter problems allow students to test themselves on what they have learned.
• Emphasizes working through the derivation of classical problems to help students understand the conceptual content of quantum mechanics and develop the analytic skills necessary to apply it.
• Contains references to popular articles appearing in Physics Today, giving students exposure to up-to-the-minute work in quantum mechanics.
Contents:
Chapter 1: Foundations • Faraday, Thomson and Electrons • Spectra, radiation and Planck • The Rutherford- Bohr Atom • de Broglie Matter-waves • Summary • Problems
Chapter 2: Schrödinger’s Equation • The classical wave equation • The time-independent Schrödinger equation • Interpretation of : Probabilities and boundary conditions • Summary • Problems
Chapter 3: Solutions of Schrödinger’s Equation in One Dimension: Part I: Potential wells • Concept of a potential well • The infinite potential well • The finite potential well • Finite rectangular well-even solutions • Number of bound states in a finite potential well • Sketching wave functions • Part II: Potential Barriers and Scattering • Potential barriers • Penetration of arbitrarily shaped barriers • Apha-decay as a barrier penetration effect • Scattering by one-dimensional potential wells • Summary • Problems
Chapter 4: Operators, Expectation Values, and the Uncertainty Principle • Properties of operators • Expectation values • The uncertainty principle • Commutators and uncertainty relations • Ehrenfest’s theorem • The Orthogonality Theorem • The superposition theorem • Constructing a time dependent wave packet • The virial theorem • Summary • Problems
Chapter 5: The Harmonic Oscillator • A lesson in dimensional analysis • The asymptotic solution• The series solution • Hermite polynomials and harmonic oscillator wavefunctions • Comparing the classical and quantum simple harmonic oscillators • Raising and lowering operators (optional) • Summary • Problems
Chapter 6: Schrödinger Equation in Three Dimensions and an Introduction to the Quantum Theory of Angular Momentum • Separation of variables: Cartesian Coordinates • Spherical coordinates • Angular momentum operators • Separation of variables in spherical coordinates: Central potentials • Angular wavefunctions and spherical harmonics
Chapter 8: Central Potentials • Introduction • The infinite spherical well • The finite spherical well • The Coulomb potential • Hydrogen atom probability distributions • The effective potential • Some philosophical remarks • Summary • Problems
Chapter 8: Further Developments with Angular Momentum and Multi-Particle Systems • Angular momentum raising and lowering operators • Problems • The Stern-Gerlach experiment: Evidence for quantized angular momentum and electronic spin • Problems • Diatomic molecules and angular momentum • Problems • Identical particles, indistinguishability and the Pauli exclusion principle • Problems
Chapter 9: Approximation Methods • The WKB method • The superposition theorem revisited • Perturbation theory • The variational method • Improving the variational method (optional) • Summary • Problems
Chapter 10: Numerical Solutions of the Schrödinger Equation • Atomic units • A straightforward numerical integration method
Chapter 11: A Sampling of Results from Time-Dependent Quantum Mechanics: Transition Rates and Probabilities • Transition frequencies • Transition rules • The sudden approximation • Summary • Problems
Appendix A: Miscellaneous Derivations • Appendix B: Answers to Selected Problems • Appendix C: Integrals and Trigonometric Identities • Appendix D: Physical ConstantsISBN - 9789380108247
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Pages : 436
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