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Terry s Archive Online

On the Quantum Mechanics of Collision Processes [English Translation]

Max Born

Published Sep 2, 2021• 0 citations
Publisher

Abstract

An examination of collision processes indicates that Schrödinger’s quantum mechanics describes not only stationary states, but also quantum jumps.
DOI
10.48034/20210828

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If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved. E. Schrödinger Introduction I have borrowed the title of a characteristic paper by Schrödinger (Schrödinger, 1952). In it he contrasts the smooth evolution of the Schrödinger wavefunction with the erratic behaviour of the picture by which the wavefunction is usually supplemented, or ‘interpreted’, in the minds of most physicists. He objects in particular to the notion of ‘stationary states’, and above all to ‘quantum jumping’ between those states. He regards these concepts as hangovers from the old Bohr quantum theory, of 1913, and entirely unmotivated by anything in the mathematics of the new theory of 1926. He would like to regard the wavefunction itself as the complete picture, and completely determined by the Schrödinger equation, and so evolving smoothly without ‘quantum jumps’. Nor would he have ‘particles’ in the picture. At an early stage, he had tried to replace ‘particles’ by wavepackets (Schrödinger, 1926). But wavepackets diffuse. And the paper of 1952 ends, rather lamely, with the admission that Schrödinger does not see how, for the present, to account for particle tracks in track chambers … nor, more generally, for the definiteness, the particularity, of the world of experience, as compared with the indefiniteness, the waviness, of the wavefunction. It is the problem that he had had (Schrödinger, 1935 a ) with his cat. He thought that she could not be both dead and alive.
Physically the examined perturbation problem can be regarded as a set of collision events of a time-independent perturbation potential with a quantum system. As an effect of collisions there is an expected definite change of energy of an initially unperturbed state of the system to some stationary perturbed state. The collision process certainly occupies some intervals of time which, however, do not enter the formalism. A striking property is the result of a choice of the sequence of collisions according to the applied circular scale of time: the scale produces almost automatically the energy terms predicted by the Schrödinger perturbation theory which usually is attained in virtue of complicated mathematical transformations. Beyond of the time scale and its rules—strictly connected with the perturbation order N introduced by Schrödinger—a partition process of the number N-1 is applied. This process, combined with contractions of the time points on the scale, provides us precisely with the perturbation terms entering the Schrödinger theory.