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Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner emphasising applications in solid state electronics and modern optics. Following a logical sequence, the book is focused on the key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on… More from these basic concepts to discuss some of the most important applications in modern semiconductor electronics and optics. Containing many homework problems and worked examples, the book is suitable for senior-level undergraduate and graduate level students in electrical engineering, materials science and applied physics.Less

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Book details

Copyright year: 2005 Publisher: Cambridge University Press Publication date: 6/23/2005 Binding: Hardcover Pages: 222 Size: 7.00" wide x 10.00" long x 0.75" tall Weight: 1.342 Language: English

AuthorTable of Contents

Preface

Classical mechanics vs. quantum mechanics

Brief overview of classical mechanics

Overview of quantum mechanics

Basic postulates and mathematical tools

State functions (Postulate 1)

Operators (Postulate 2)

Equations of motion (Postulate 3)

Eigen functions, basis states, and representations

Alternative notations and formulations

Problems

Wave/particle duality and de Broglie waves

Free particles and de Broglie waves

Momentum representation and wave packets

Problems

Particles at boundaries, potential steps, barriers, and in quantum wells

Boundary conditions and probability currents

Particles at a potential step, up or down

Particles at a barrier and the quantum mechanical tunneling effect

Quantum wells and bound states

Three-dimensional potential box or quantum well

Problems

The harmonic oscillator and photons

The harmonic oscillator based on Heisenberg's formulation of quantum mechanics

The harmonic oscillator based on Schrodinger's formalism

Superposition state and wave packet oscillation

Photons

Problems

The hydrogen atom

The Hamiltonian of the hydrogen atom

Angular momentum of the hydrogen atom

Solution of the time-independent Schrodinger equation for the hydrogen atom

Structure of the hydrogen atom

Electron spin and the theory of generalized angular momentum

Spin-orbit interaction in the hydrogen atom

Problems

Multi-electron ions and the periodic table

Hamiltonian of the multi-electron ions and atoms

Solutions of the time-independent Schrodinger equation for multielectron ions and atoms

The periodic table

Problems

Interaction of atoms with electromagnetic radiation

Schrodinger's equation for electric dipole interaction of atoms with electromagnetic radiation

Time-dependent perturbation theory

Transition probabilities

Selection rules and the spectra of hydrogen atoms and hydrogen-like ions

The emission and absorption processes

Light Amplification by Stimulated Emission of Radiation (LASER) and the Einstein A- and B-coefficients

Problems

Simple molecular orbitals and crystalline structures

Time-independent perturbation theory

Covalent bonding of diatomic molecules

sp, sp[superscript 2], and sp[superscript 3] orbitals and examples of simple organic molecules

Diamond and zincblende structures and space lattices

Problems

Electronic properties of semiconductors and the p-n junction

Molecular orbital picture of the valence and conduction bands of semiconductors

Nearly-free-electron model of solids and the Bloch theorem

The k-space and the E vs. k diagram

Density-of-states and the Fermi energy for the free-electron gas model

Fermi-Dirac distribution function and the chemical potential

Effective mass of electrons and holes and group velocity in semiconductors

n-type and p-type extrinsic semiconductors

The p-n junction

Problems

The density matrix and the quantum mechanic Boltzmann equation

Definitions of the density operator and the density matrix

Physical interpretation and properties of the density matrix

The density matrix equation or the quantum mechanic Boltzmann equation

Examples of the solutions and applications of the density matrix equations

Problems

References

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