Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T21:37:31.929Z Has data issue: false hasContentIssue false

On the Principle of Superposition in Quantum Mechanics

Published online by Cambridge University Press:  20 November 2018

G.F.D. Duff*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. de Broglie, L. and Brillouin, L., Selected papers on wave mechanics. London, 1928.Google Scholar
2. Dirac, P.A.M., Principles of Quantum Mechanics. 3rd ed., Oxford, 1947.Google Scholar
3. Gårding, L., Linear hyperbolic differential equations with constant coefficients. Acta Mathematica, 85 (1951), 162.Google Scholar
4. Gelfand, I. M. and Shilov, G. E., Fourier transforms of rapidly increasing functions and questions of the uniqueness of the solution of Cauchy's problem. Uspehi Mat. Nauk(N. S.) 8, (58), (1953), p. 354. (A. M. S. trans. ser. 2, vol. 5. )Google Scholar
5. Schrödinger, E., Collected papers on wave mechanics. London, 1928.Google Scholar