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Zeitschrift für Physikalische Chemie

Quantum Mechanics, Special Chapters

GERD RÖPKE

Published Feb 1, 1999• 15 citations
Publisher
DOI
10.1524/zpch.1999.213.part_2.223

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Preface (with Browser Tests and System Requirements) Chapter 1: Introduction to Physlets Part 1: Special Relativity Chapter 2: Space and Time in Special Relativity Chapter 3: Relativistic Mechanics Part 2: The Need for a Quantum Theory Chapter 4: From Blackbody to Bohr Chapter 5: Wave-Particle Duality Part 3: Quantum Theory Chapter 6: Classical and Quantum-mechanical Probability Chapter 7: The Schrodinger Equation Chapter 8: The Free Particle Chapter 9: Scattering in One Dimension Chapter 10: The Infinite Square Well Chapter 11: Finite Square Wells and Other Piecewise-constant Wells Chapter 12: Harmonic Oscillators and Other Spatially-varying Wells Chapter 13: Multi-dimensional Wells Part 4: Applications Chapter 14: Atomic, Molecular, and Nuclear Physics Chapter 15: Statistical Mechanics
Relativistic quantum mechanics is the unification into a consistent theory of Einstein's theory of relativity and the quantum mechanics of physicists such as Bohr, Schrödinger, and Heisenberg. Evidently, to appreciate relativistic quantum theory it is necessary to have a good understanding of these component theories. Apart from this chapter we assume the reader has this understanding. However, here we are going to recall some of the important points of the classical theory of special relativity. There is good reason for doing this. As you will discover all too soon, relativistic quantum mechanics is a very mathematical subject and my experience has been that the complexity of the mathematics often obscures the physics being described. To facilitate the interpretation of the mathematics here, appropriate limits are taken wherever possible, to obtain expressions with which the reader should be familiar. Clearly, when this is done it is useful to have the limiting expressions handy. Presenting them in this chapter means they can be referred to easily. Taking the above argument to its logical conclusion means we should include a chapter on non-relativistic quantum mechanics as well. However, that is too vast a subject to include in a single chapter. Furthermore, there already exists a plethora of good books on the subject.
Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.