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A consistency condition for electron wave functions

Published online by Cambridge University Press:  24 October 2008

C. Jayaratnam Eliezer
C. Jayaratnam Eliezer
Affiliation:
Mathematics Department, University of Ceylon, Colombo 3, Ceylon
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Extract

Dirac's wave equation of an electron enables one to solve for the wave function of an electron moving in an electromagnetic field. The wave function ψ has 4 components ψ1, ψ2, ψ3, ψ4, and the electromagnetic field is described by a four-vector Aμ, consisting of a scalar potential φ and a vector potential A.

In the usual problem, we solve for the wave function ψ when the potential Aμ is given. By doing so, we obtain the wave function of an electron which moves in a given electromagnetic field. It is of some interest to consider the reverse question: given the wave function ψ, what can we say about the electromagnetic potential Aμ, which is connected with ψ by Dirac's equation? Is Aμ uniquely determined, and if not, what is the extent to which it is arbitrary ?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 247 - 250
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCE

(1)Dirac, P. A. M.Quantum Mechanics (Oxford, 1947), p. 256.Google Scholar