# Fundamentals of Quantum Mechanics

#### By **Sakir Erkoc**

Taylor & Francis – 2006 – 433 pages

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.

". . . the book provides sufficient breadth and depth both to familiarize the reader with the basic ideas and mathematical expressions of quantum mechanics and to form the basis for deeper understanding later . . . The material is lavishly illustrated by pictures and graphics . . . a good example of a compact textbook on a very complicated area of physics."

-- Michael B. Mensky, in Zentralblatt Math, 2009

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

INELASTIC SCATTERING

Bibliography and References 409

Appendix 413

Index 417

Name: Fundamentals of Quantum Mechanics (Hardback) – Taylor & Francis

Description: By Sakir Erkoc. 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...

Categories: Quantum Mechanics