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Published online by Cambridge University Press: 24 October 2008
In three earlier papers the author has developed the theory of the operational wave equation, which was originally suggested by Professor Eddington as the most extensive generalisation possible of the linear wave equation devised by Dirac. The wave function,ψ, plays a very minor rô1e in the development of this theory and, in reality, it is introduced simply to provide an operand which shall be patient of the action of the wave operators, A1, A2, A3, A4. The object of this paper is to show that the wave function may be entirely eliminated from the theory, which then takes the form of a “ matrix mechanics,” i.e. a set of relations between matrices representing the coordinates, the momenta and the spin operators.
* Proc. Roy. Soc., A, Vol. 127, pp. 339 and 349, and Vol. 128, p. 47 (1930). Quoted here as Papers I, II and III.CrossRefGoogle Scholar
† These are the momentum operator M3, the interaction operator Q, and the energy operator p0. The wave operator W, is, of course, also reducible, but since its eigen value is always zero it does not serve to distinguish between different wave functions.
* Born and Jordan, Elementare Quantenmechanik, § 32.