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Mathematical Proceedings of the Cambridge Philosophical Society

A remark on quantum-mechanical perturbation theory

Nicholas Kemmer

Published Oct 1, 1954• 0 citations
Publisher

Abstract

In the course of preparing lectures on elementary quantum theory the author developed a way of presenting time-independent perturbation theory that seems to have some advantages over more familiar presentations. There is nothing fundamentally new in the method, and if any claim of greater power can be made for the new version, it is at best for situations in which high-order perturbations are of interest. Quantum-field theorists will no doubt recognize the relation of this presentation to much that has been done in their subject recently.

DOI
10.1017/s0305004100029777

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In the course of preparing lectures on elementary quantum theory the author developed a way of presenting time-independent perturbation theory that seems to have some advantages over more familiar presentations. There is nothing fundamentally new in the method, and if any claim of greater power can be made for the new version, it is at best for situations in which high-order perturbations are of interest. Quantum-field theorists will no doubt recognize the relation of this presentation to much that has been done in their subject recently.
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In 1925-26, the late Max Born gave two sets of lectures at M.I.T., one on the structure of the atom, the other on the lattice theory of rigid bodies. Problems of Atomic Dynamics contains the text of both sets.What gives this volume its remarkable interest is just those dates: 1925-26. This must have been, by all accounts, the headiest period in twentieth-century physics, and Max Born was one of the leaders of the ferment. As Norbert Wiener remembers, When Professor Born came to the United States [for these lectures in 1925] he was enormously excited about the basis Heisenberg had just given for the quantum theory of the atom.These lectures represent perhaps the most vivid written record of the transition between the old quantum theory of Bohr, and the new theory. At the time I began this course of lectures, Born writes, first paper on the quantum theory had just appeared. Here his masterly treatment gave the quantum theory an entirely turn. The paper of Jordan and myself, in which we recognized the matrix calculus as the proper formulation of Heisenberg's ideas, was in press, and the manuscript of a third paper by the three of us was almost completed.Even as the lecture series progressed, Born became familiar with results, which he introduced into his presentation: Pauli's fourth quantum number, Dirac's formalism, his own work on a general operational calculus. And yet, in spite of the conditions of revolutionary changes in physics that year -- in which established ancien regime principles were collapsing almost monthly -- the theory is developed with a cool elegance and with a formal completeness which may be regarded as a limiting case of its current state. These lectures represent the foundations of quantum theory, and they have withstood the tests of time -- the tests of more than forty years of experimental evidence.
ENERAL philosophy claims to be the critical subject which lays down for all of us what we may be allowed to think, and yet it has played no part whatever in the great revolutions of human thought of the present century-those connected with relativity and the quantum theory. It might have been expected that the scientists would have been constantly consulting the philosophers as to the legitimacy of their various speculations, but nothing of the kind has happened. Since no one can dispense with some sort of metaphysic, each scientist has made one for himself, and no doubt they contain many crudities, but it would seem that a deep interest in metaphysic is a disadvantage rather than an advantage to the physicist-at least I have the impression that those of my friends who are most inclined to speculate on the ultimate things appear to be the ones whose scientific work is most hampered by doing so. Now I propose to risk a similar indiscretion. I want to embody in it the practical philosophy of a physicist, and I do not mean it as an attack on the pure philosophers, who are very reasonable people, only chargeable with the minor offence of not having made me want to read their books! I had better begin by stating shortly the ideas I intend to discuss. There is a notable contrast between the way we think about things and the way we think we ought to think about them.