Book contents
- Frontmatter
- Contents
- Preface
- Recollections of an Independent Thinker
- A Look Back: Early Applications of Maximum Entropy Estimation to Quantum Statistical Mechanics
- The Jaynes–Cummings Revival
- The Jaynes–Cummings Model and the One-Atom-Maser
- The Jaynes–Cummings Model is Alive and Well
- Self-Consistent Radiation Reaction in Quantum Optics – Jaynes' Influence and a New Example in Cavity QED
- Enhancing the Index of Refraction in a Nonabsorbing Medium: Phaseonium Versus a Mixture of Two-Level Atoms
- Ed Jaynes' Steak Dinner Problem II
- Source Theory of Vacuum Field Effects
- The Natural Line Shape
- An Operational Approach to Schrödinger's Cat
- The Classical Limit of an Atom
- Mutual Radiation Reaction in Spontaneous Emission
- A Model of Neutron Star Dynamics
- The Kinematic Origin of Complex Wave Functions
- On Radar Target Identification
- On the Difference in Means
- Bayesian Analysis, Model Selection and Prediction
- Bayesian Numerical Analysis
- Quantum Statistical Inference
- Application of the Maximum Entropy Principle to Nonlinear Systems Far from Equilibrium
- Nonequilibrium Statistical Mechanics
- A Backward Look to the Future
- Appendix: Vita and Bibliography of Edwin T. Jaynes
- Index
The Classical Limit of an Atom
Published online by Cambridge University Press: 21 October 2009
- Frontmatter
- Contents
- Preface
- Recollections of an Independent Thinker
- A Look Back: Early Applications of Maximum Entropy Estimation to Quantum Statistical Mechanics
- The Jaynes–Cummings Revival
- The Jaynes–Cummings Model and the One-Atom-Maser
- The Jaynes–Cummings Model is Alive and Well
- Self-Consistent Radiation Reaction in Quantum Optics – Jaynes' Influence and a New Example in Cavity QED
- Enhancing the Index of Refraction in a Nonabsorbing Medium: Phaseonium Versus a Mixture of Two-Level Atoms
- Ed Jaynes' Steak Dinner Problem II
- Source Theory of Vacuum Field Effects
- The Natural Line Shape
- An Operational Approach to Schrödinger's Cat
- The Classical Limit of an Atom
- Mutual Radiation Reaction in Spontaneous Emission
- A Model of Neutron Star Dynamics
- The Kinematic Origin of Complex Wave Functions
- On Radar Target Identification
- On the Difference in Means
- Bayesian Analysis, Model Selection and Prediction
- Bayesian Numerical Analysis
- Quantum Statistical Inference
- Application of the Maximum Entropy Principle to Nonlinear Systems Far from Equilibrium
- Nonequilibrium Statistical Mechanics
- A Backward Look to the Future
- Appendix: Vita and Bibliography of Edwin T. Jaynes
- Index
Summary
ABSTRACT. A series of recent experiments and calculations are described that study the classical limit of an atom. The classical limit of an atom is defined to be the quantum mechanical state that most nearly approximates the ideal of a classical particle traveling in a Kepler orbit. It is found that correspondence between the quantum and classical descriptions is always in the form of ensembles of many realizations so long as the electron is taken to be a point particle. Even in the limit of a wave packet made up of states with all quantum numbers large there are distinctly quantum interference features in the evolution of the quantum ensemble. However, when the classical theory is modified by allowing within the ensemble only the Kepler orbits corresponding to energies and angular momenta allowed by Bohr's old quantum theory, most of the interference features are produced by the ensemble of classical particles.
Ed Jaynes has been characterized variously as a physicist, a statistician, an inventor, a free thinker, a teacher, a mentor, and a rabble rouser. It is hard to dispute his right to any of these mantles he might wish to claim, but it is equally hard to find a finite set of descriptors that do him justice. From my own selfish point of view his most important contribution has been to act as a source of ideas and new ways of looking at some long-standing and fundamental problems.
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- Chapter
- Information
- Physics and ProbabilityEssays in Honor of Edwin T. Jaynes, pp. 117 - 126Publisher: Cambridge University PressPrint publication year: 1993