Fundamentals of Quantum Mechanics

895.00

  • Author: Sakir Erkoc
  • Publisher: Taylor & Francis
  • ISBN-13: 9781584887331
  • Pages: 433
  • Binding: Paperback
  • Year of Pub / Reprint Year: 2007
Category:

Description

About The Book

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.

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 Schrödinger Equation
The Simple Harmonic Oscillator
Unbound States
One-Dimensional Barrier Problems
The Finite Potential Well

N-PARTICLE SYSTEMS
The Schrödinger Equation for N-Particle Systems
Identical Particles
The Pauli Principle; Fermions and Bosons

THE SCHRÖDINGER EQUATION IN THREE-DIMENSIONS
The Two-Body Systems
Separation of Variables in the Two-Body Systems
Rotational Invariance
The Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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

Features:

Presents a unified account of nonrelativistic quantum mechanics
Covers the historical basis and mathematical foundations of nonrelativistic quantum theory
Examines the fundamentals of quantum theory in three dimensions
Contains approximation methods used in quantum mechanics and scattering theory
Includes applications, worked examples, and homework problems
Provides a complete source of approximation methods for quantum mechanics