Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T14:00:52.056Z Has data issue: false hasContentIssue false

The characterization of quantum-mechanical operators

Published online by Cambridge University Press:  24 October 2008

J. L. B. Cooper
Affiliation:
Birkbeck CollegeLondon

Extract

It is well known that the operators mainly employed in quantum theory are hermitian; it is less well known amongst physicists that they are required, in addition, to be self-adjoint. This is essential for the validity of the result known in quantum theory as the representation theorem and in the mathematical theory as the resolution of the identity. The purpose of this paper is to show that the self-adjoint operators can be characterized by a condition which is nearer to having a physical significance than those given in the literature.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)von Neumann, J.Math. Ann. 102 (1929), 49131.CrossRefGoogle Scholar
(2)von Neumann, J.Mathematische Grundlagen der Quanlenmechanik (Berlin, 1932).Google Scholar
(3)Stone, M. H.Linear transformations in Hilbert space (New York, 1932).Google Scholar
(4)Stone, M. H.Ann. Math. 33 (1932), 643–8.CrossRefGoogle Scholar
(5)Cooper, J. L. B.Proc. London Math. Soc. 50 (1948), 1155.CrossRefGoogle Scholar
(6)Cooper, J. L. B.Ann. Math. 48 (1947), 827–42.CrossRefGoogle Scholar
(7)Dirac, P. A. M.Principles of quantum mechanics, 2nd ed. (Oxford, 1935).Google Scholar
(8)Pauli, W.Handbuch der Physik, 2nd ed. (Berlin, 1932) 24, i.Google Scholar