# An Introduction to Quantum Physics

## A First Course for Physicists, Chemists, Materials Scientists, and Engineers

1. Edition December 2017

XXVIII, 536 Pages, Softcover

197 Pictures*Textbook*

**978-3-527-41247-1**

### Short Description

A comprehensive self-contained textbook on quantum physics and chemistry and the structure of matter at the level of an introductory and an intermediate course, with an online supplement that contains review quizzes, theory supplements, and further applications.

This book presents Quantum Mechanics as a theory underlying the world around us, from atoms and molecules to materials, lasers, and other applications. Its features are (a) emphasis on the key principles with minimal mathematical formalism, (b) use of dimensional analysis and order-of-magnitude estimates to develop intuition, (c) comprehensive overview of quantum chemistry and the electronic structure of solids, (d) extensive discussion of the basic processes of lightmatter interactions, and (e) online supplement with advanced theory and multiplechoice quizzes.

"A famous joke among physicists is that 'One does not really understand quantum mechanics, but simply gets used to it.' To an undergraduate student being exposed to quantum physics for the first time, this phrase may come very close to how it feels to speak Nature's language of the atomic scale. Trachanas' Quantum Physics aims to remove this feeling and in my opinion it succeeds brilliantly."

Efthimios Kaxiras, Harvard University

"Expertly translated, this elegant book by Stefanos Trachanas - a seasoned educator of quantum physics - offers a unique pedagogical approach to quantum mechanics by discussing novel ways to find exact solutions, exploiting useful tools such as dimensional analysis, and providing intuition and physical insight behind the results. Quantum mechanics is a complex field, but this book makes it brilliantly accessible and a delight to learn."

Nader Engheta, University of Pennsylvania

PART I: Fundamental Principles

THE PRINCIPLE OF WAVE-PARTICLE DUALITY: AN OVERVIEW

The Principle of Wave-Particle Duality of Light

The Principle of Wave-Particle Duality of Matter

Dimensional Analysis and Quantum Physics

THE SCHRÖDINGER EQUATION AND ITS STATISTICAL INTERPRETATION

INTRODUCTION: The wave-particle duality as the fundamental law of modern quantum mechanics

The Schrödinger Equation

Statistical Interpretation of Quantum Mechanics

Further Development of the Statistical Interpretation: The Mean-Value Formula

Time Evolution of Wavefunctions: Superposition States and Further Development of the Statistical Interpretation

Self-Consistency of the Statistical Interpretation and the Mathematical Structure of Quantummechanics

Summary: Quantum Mechanics in a Nutshell

THE UNCERTAINTY PRINCIPLE

The Position-Momentum Uncertainty Principle

The Time-Energy Uncertainty Principle

The Uncertainty Principle in the Classical Limit

General Investigation of the Uncertainty Principle

PART II. Simple Quantum Systems

SQUARE POTENTIALS I

Particle in a One-Dimensional Box: The Infinite Potential Well

The Square Potential Well

SQUARE POTENTIALS II

The Square Potential Step: Reflection and Transmission

Rectangular Potential Barrier: Tunneling Effect

THE HARMONIC OSCILLATOR

Solution of the Schrödinger Eequation

Discussion of the Results

A Plausible Question: Can we use the Polynomial Method to Solve Potentials other than the Harmonic Oscillator?

THE POLYNOMIAL METHOD

Sufficient Conditions for the Existence of Polynomial Solutions: Bidimensional Equations

The Polynomial Mehtod in Action: Exact Solution of the Krätzer and Morse Potentials

Mathematical Afterword

THE HYDROGEN ATOM I

Solving the Schrödinger Equation for the Spherically Symmetric Eigenfunctions

Discussion of the Results

What is the Electron Doing in the Hydrogen Atom after all? A First Discussion on the Basic Questions of Quantum Mechanics

THE HYDROGEN ATOM II

The Schrödinger Equation in an Arbitrary Central Potential: The Method of Separation of Variables

The Hydrogen Atom

ATOMS IN A MAGNETIC FIELD - THE EMERGENCE OF SPIN

Atomic Electrons as Microscopiy Magnets: Magnetic Moment and Angular Momentum

The Zeeman Effect and the Evidence for the Existence of Spin

The Stern-Gerlach Experiment: Unequivocal Experimental Confirmation of the Existence of Spin

What is Spin?

Time Evolution of Spin in a Magnetic Field

Total Angular Momentum of Atoms: Addition of Angular Momenta

IDENTICAL PARTICLES AND THE PAULI PRINCIPLE

The Principle of Indistinguishability of Identical Particles in Quantum Mechanics

Indistinguishability of Identical Particles and the Pauli Principle

The Role of Spin: Complete Formulation of the Pauli Principle

The Pauli Exclusion Principle

Which Particles are Fermions and Which are Bosoms

Exchange Degeneracy: The Problem and its Solution

PART III. Quantum Mechanics in Action: Structure of Matter

ATOMS

Arrangement of Energy Levels in Many-Electron Atoms: The Screening Effect

Quantum Mechanical Explanation of the Periodic Table: The "Small Periodic Table"

Approximate Calculations in Atoms: Perturbation Theory and the Variational Method

MOLECULES I

The Double-Well Model of Chemical Bonding

Examples of Simple Molecules

Molecular Spectra

MOLECULES II

Hybridization: The First Basic Deviation from the Elementary Theory of the Chemical Bond

Delocalization: The Second Basic Deviation from the Elementary Theory of the Chemical Bond

SOLID STATE

Periodicity and Band Structure

Band Structure and the "Mystery of Conductivity." Conductors, Semiconductors, Insulators

Crystal Momentum, Effective Mass, and Electron Mobility

Fermi Energy and Density of States

MATTER AND LIGHT

The Four Fundamental Processes: Resonance, Scattering, Ionization, and Spontaneous Emission

Quantitative Description of the Fundamental Processes: Transition Rate, Effective Cross Section, Mean Free Path

Matter and Light in Resonance. I: Theory

Matter and Light in Resonance. II: The laser

Spontaneous Emission

Theory of Time-Dependent Perturbations: Fermi's Rule

The Light Itself: Polarized Photons and their Quantum Mechanical Description

Manolis Antonoyiannakis is an Associate Editor and Bibliostatistics Analyst at the American Physical Society, and an Adjunct Associate Research Scientist at the Department of Applied Physics & Applied Mathematics at Columbia University, USA. He received his PhD from Imperial College London, UK. His editorial experience in the Physical Review journals stimulated his interest in statistical, sociological, and historical aspects of peer review, but also in scientometrics and information science. He is currently developing data science tools to analyze scientific publishing and enhance research assessment.

Leonidas Tsetseris is an Associate Professor at the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens, Greece. He obtained his PhD from the University of Illinois at Urbana-Champaign, USA. His research expertise is on computational condensed matter physics and materials science, particularly quantum-mechanical studies on emerging materials. He has taught a variety of university courses, including classical mechanics, electromagnetism, quantum mechanics, and solid state physics.