An Introduction to Quantum Physics

Foreword
 
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

Stefanos Trachanas is an educator, author, and publisher. For over 35 years he has taught most of the core undergraduate courses at the Physics Department of the University of Crete. His books on quantum mechanics and differential equations are used as primary textbooks in most Greek University Departments of Physics, Chemistry, Materials Science, and Engineering. He is a cofounder of Crete University Press, which he led as Director from 1984 until his retirement in 2013. His awards include an honorary doctorate from the University of Crete, the Xanthopoulos-Pnevmatikos national award for excellence in academic teaching, and the Knight Commander of the Order of Phoenix, bestowed by the President of Greece.
 
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.