HYDROGEN ATOM, THE

This book provides a comprehensive exploration in the fundamental physics of the non-relativistic atom in terms of its symmetries. The book gives a complete treatment of the dynamical symmetries of the H atom and the use of these symmetries to determine energy levels and analytically calculate the first order radiative Lamb shift using group theory. Understanding radiative shifts is critical since measurement of the Lamb shift led to the development of quantum electrodynamics. The harmony between the mathematics and the physics is emphasised throughout the book. Through the lens of symmetry, it is possible to elucidate key features of the H atom in a way that is elegant, simple, and focuses on fundamentals.

Understanding the hydrogen atom has been the gateway to the development of quantum physics for over 100 years. Both quantum mechanics and quantum electrodynamics were discovered by exploring the spectra of the H atom. This book outlines the key mathematical and physical behavior of the H atom, and its historical context, that led to these discoveries. The quantum behavior is related to the corresponding classical behavior and to the harmonic oscillator, the other fundamental central force system. Understanding the H atom, the most basic physical system, is a gateway to understanding much of quantum theory.

Contents:

• Preface
• Symmetry and Degeneracy of Energy Levels in a Coulomb Potential:
  • Introduction to the H Atom and Symmetry Principles
  • Classical Theory of the H Atom
  • The Hydrogen-like Atom in Quantum Mechanics
  • Wave Functions for the Hydrogen-like Atom
  • The Dirac Hydrogen Atom: The Kepler Problem for a Relativistic Spinning Electron
• The Coulomb Potential and Non-invariance Groups:
  • The Spectrum Generating Group SO(4,1) for the Hydrogen-like Atom
  • The Group SO(4,2)
• Radiative Level Shifts:
  • History and Some Aspects of the Lamb Shift
  • Radiative Shifts, Classical Physics, and the Zero-Point Fluctuations of the Electromagnetic Field
  • The Radiative Shift in Field Theory
  • Calculation of the Radiative Shifts in the Non-relativistic Approximation
  • SO(4,2) Calculation of the Radiative Shift for the Schrodinger Hydrogen Atom
  • Radiative Shift of a Relativistic Meson (Spinless Electron) in a Harmonic Potential
  • New Insights into the Lamb Shift: The Spectral Density of the Shift
  • The Cloud of Virtual Quanta Surrounding the H Atom
• Appendix: Brief Derivation of the Group Theoretical Formula for the Radiative Shift
• References
• Index

Readership: The primary market is advanced undergraduate and graduate students and researchers who want to learn about atomic physics, quantum physics and quantum field theory using the hydrogen atom as a foundation, and who are interested in the symmetries of the atom and how they may be used to understand and facilitate analytical calculations of the radiative shifts and other properties. This book could be a supplementary text in a quantum mechanics course or in a field theory course, or a course dealing with symmetries in physical systems.