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Development of Quantum Theory from Physical Principles-Quantum Mechanics Without Waves

Author:

Robert T. Deck

ISBN:

978-1-940366-80-7

Publisher:

Science Publishing Group

SEMI-OPEN ACCESS

Table of Contents

Preface

Introduction

Chapter 1 Principle of Uncertainty

1 Underlying Basis of Principle

2 Statement of Principle

3 Auxiliary Concepts Associated with Principle

4 Formulation of Principle

4.1 Basis for Formulation (Quantum Formalism)

4.2 Method of Formulation

(1) Superposition Relation for Kets

(2) Commutation Relations for Operators

4.3 Alternative Method of Formulation

5 Consequences of Principle

Chapter 2 Principle of Invariance

1 Underlying Basis of Principle

2 Statement of Principle

2.1 General Statement of Principle

2.2 Quantitative Statements of Principle

3 Formulation of Principle of Invariance

3.1 Basis for Formulation of Principle

3.2 Physical Content of Formulation

Chapter 3 Detailed Formulation of Invariance Principle

1 Space Translation Operator

2 Space Rotation Operator

3 Lorentz Boost Operator

4 Space Inversion Operator

5 Time Reversal Operator

Chapter 4 Applications of Principles to Description ofInteractions(Non-relativistic Theory)

1 Form of Equations of Motion and Related Eigenvalue Equations

2 Methods for Solution of Equations of Motion and Related Eigenvalue Equations

2.1 Qualitative Methods

2.2 Exact Methods: Solution of Exactly Solvable Equations

2.3 Approximate Methods

Chapter 5 Application of Principles to Derivation of Relativistic Equation of Motion

1 Equation of Motion for Free Particle (Dirac Equation)

2 Equation of Motion for Interacting Particle

Chapter 6 Applications of Equation of Motion and Related Hamiltonian

1 Solution of Dirac Equation for Central Potential

2 Description of Non-Relativistic Electron in Uniform Magnetic Field

3 Description of Atomic Electron

4 Description of Atomic Electron in External Magnetic Field

Chapter 7 Principle of Identical Particle Indistinguishability

1 Statement and Formulation of Principle

1.1 Basis for Principle

1.2 Statement of Principle

1.3 Formulation of Principle

2 Consequences of Principle

3 Applications of Principle

Epilogue

Author(s)

Robert T. Deck, received his PhD in theoretical physics from the University of Notre Dame with a specialty in quantum electrodynamics and particle physics. He then held a postdoctoral position at the University of Michigan before assuming a faculty position at the University of Toledo. There, his lectures in a variety of theory courses including all levels of Quantum Mechanics earned him an outstanding teaching award. He is currently an emeritus professor of physics at Toledo where he works in the areas of optics and photonics. The present book is a testament to his career long interest in the foundations of Quantum Mechanics.

Description

Book develops the equations of quantum mechanics from two principles:

(1) A general statement of the Uncertainty Principle that recognizes the existence in nature of pairs of incompatible observables, the simultaneous values of which have irreducible intrinsic uncertainties, the product of which is constrained by a fundamental constant of nature, Planck’s constant.

(2) The Invariance Principle, which requires that the equations (laws) of physics have the same form in all physically equivalent coordinate frames.

The latter principle is used to uniquely derive all the known specific uncertainty relations from the general uncertainty principle as shown in author’s paper

**"A Formulation of Quantum Theory Based on Two Physical Principles" R.T. Deck, Journal of Modern Physics, January 2015. (Also online in SciRes. at http://www.scrip.org/journal/jmp, http://dx.doi.org/10.4236/jmp.2014.)**

(Copy of paper will be sent on request.)

In addition Book provides an explanation of the Spin-Statistics Theorem.

Additional unique features are stated in the Overview of the Book sent as an attachment.

(1) A general statement of the Uncertainty Principle that recognizes the existence in nature of pairs of incompatible observables, the simultaneous values of which have irreducible intrinsic uncertainties, the product of which is constrained by a fundamental constant of nature, Planck’s constant.

(2) The Invariance Principle, which requires that the equations (laws) of physics have the same form in all physically equivalent coordinate frames.

The latter principle is used to uniquely derive all the known specific uncertainty relations from the general uncertainty principle as shown in author’s paper

(Copy of paper will be sent on request.)

In addition Book provides an explanation of the Spin-Statistics Theorem.

Additional unique features are stated in the Overview of the Book sent as an attachment.