Fundamentals of Quantum Mechanics
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Fundamentals of Quantum Mechanics

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Providing a unified account of nonrelativistic quantum mechanics, Fundamentals of Quantum Mechanics covers the principles and formalism of quantum mechanics and the development and application of general techniques for the solution of quantum mechanical problems. The author has done everything possible to make the math in this book accessible. The book is divided into three parts. The first part provides the historical basis and mathematical foundations on nonrelativistic quantum theory. The physical systems considered in this part are mainly in one dimension. The second part covers the fundamentals of quantum theory in three dimensions. Many-particle systems, the motion of a particle in three dimensions, angular and spin momenta, interaction of a charged particle with external fields, and matrix mechanical formulation of quantum mechanics are discussed in this part. The third part contains the approximation methods used in quantum mechanics and scattering theory. Carefully designed to cover the entire topic, the book provides sufficient breadth and depth both to familiarize readers with the basic ideas and mathematical expressions of quantum mechanics and to form the basis for deeper understanding.show more

Product details

  • Hardback | 433 pages
  • 157.5 x 238.8 x 30.5mm | 498.96g
  • Taylor & Francis Ltd
  • London, United Kingdom
  • English
  • 125 black & white illustrations
  • 158488732X
  • 9781584887324

Table of contents

HISTORICAL EXPERIMENTS AND THEORIES Dates of Important Discoveries and Events Blackbody Radiation Photoelectrice Effect Quantum Theory of Spectra TheComptone Effect Matterwaves, the de Broglie Hypothesis The Davisson -Germer Experiment Heisenberg's Uncertainity Principle Difference Between Particles and Waves Interpretation of the Wavefunction AXIOMATIC STRUCTURE OF QUANTUM MECHANICS The Necessity of Quantum Theory Function Spaces Postulates of Quantum Mechanics The Kronecker Delta and the Dirac Delta Function Dirac Notation OBSERVABLES AND SUPERPOSITION Free Particle Particle In A Box Ensemble Average Hilbert -Space Interpretation The Initial Square Wave Particle Beam Superposition and Uncertainty Degeneracy of States Commutators and Uncertainty TIME DEVELOPMENT AND CONSERVATION THEOREMS Time Development of State Functions, The Discrete Case The Continuous Case, Wave Packets Particle Beam Gaussian Wave Packet Free Particle Propagator The Limiting Cases of the Gaussian Wave Packets Time Development of Expectation Values Conservation of Energy and Momentum Conservation of Parity BOUND AND UNBOUND STATES IN ONE-DIMENSION One-Dimensional Schrodinger Equation The Simple Harmonic Oscillator Unbound States One-Dimensional Barrier Problems The Finite Potential Well N-PARTICLE SYSTEMS The Schrodinger Equation for N-Particle Systems Identical Particles The Pauli Principle; Fermions and Bosons THE SCHRODINGER EQUATION IN THREE-DIMENSIONS The Two-Body Systems Separation of Variables in the Two-Body Systems Rotational Invariance The Schrodinger Equation for Non-Central Potentials ANGULAR MOMENTUM Commutation Relations Raising and Lowering Operators Eigen Solutions of Angular Momentum Operators Kinetic Energy and Angular Momentum THE RADIAL EQUATION FOR FREE AND BOUND PARTICLES The Radial Schrodinger Equation The Free Particle Three-Dimensional Square Well Potential The Hydrogenatom The Spectra of Hydrogenic Atoms The Virial Theorem INTERACTION OF ELECTRONS WITH ELECTROMAGNETIC FIELD Maxwell 's Equations and Gauge Transformations Motion of a Free Electron in a Uniform Magnetic Field Motion of a Bound Electron in a Uniform Magnetic Field The Principal of Gauge Invariance and Flux Quantization MATRIX REPRESENTATIONS Matrix Representations of Wave Functions and Operators Matrix Algebra Types of Matrix Representations Harmonic Oscillator in Matrix Representations Matrix Representations of Angular Momentum Operators SPIN AND THE ADDITION OF ANGULAR MOMENTA Systems with Spin One-Half The Addition of Angular Momenta TIME-INDEPENDENT PERTURBATION THEORY Nondegenerate Perturbation Theory Degenerate Perturbation Theory THE VARIATIONAL METHOD The Variational Principle Linear Variation Functions THE WKB APPROXIMATION Turning Points The Connection Formulas The WKB Approximation to a Potential Well The WKB Approximation to a Potential Barrier TIME-DEPENDENT PERTURBATION THEORY Time -Dependent Schrodinger Equation Time -Dependent Perturbation Approximations Sinusoidal Perturbations Emission and Absorption of Radiation Incoherent Perturbations Selection Rules THE ADIABATIC APPROXIMATION The Adiabatic Processes The Adiabatic Theorem Nonholonomic Processes Experimental Evidences of Nonholonomic Processes PATH-INTEGRATION METHOD An Approximation to Time -Evolution for a Free Particle Path Integral Evaluation of the Free Particle Propagator Equivalence to the Schrodinger Equation SCATTERING THEORY Classical Scattering Theory Center-of-Mass and Laboratory Frames Quantum Scattering Theory The Method of Partial waves (Low -Energy Case) Expansion of a Plane Wave into Spherical Waves Expansion of the Scattering Amplitude Scattering from a Delta Potential Scattering from a Square -Well Potential Scattering from a Hardsphere Scattering of Identical Particles Energy Dependence and Resonance Scattering The Lippman-Schwinger Equation (High-Energy Case) The Greens Function for the Scattering Problem Born Approximation INELASTIC SCATTERING Bibliography and References 409 Appendix 413 Index 417show more

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