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Certain Expansions in the Algebra of Quantum Mechanics1

Published online by Cambridge University Press:  20 January 2009

Neal H. McCoy
Neal H. McCoy
Affiliation:
Smith College, Northampton, Mass., U.S.A.
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§ 1. Introduction. The algebra of quantum mechanics is characterized by the fact that the variables p, q obey all the laws of ordinary algebra except that multiplication is non-commutative and instead there exists a relation of the form

where c is a real or complex scalar constant and is thus commutative with both p and q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 2 , July 1932 , pp. 118 - 127
Copyright
Copyright © Edinburgh Mathematical Society 1932

References

page 118 note 1 Some of the results presented here were obtained while the author was a National Research Fellow at Princeton University.

page 118 note 2 For references to this algebra see a previous paper. Transactions of the American Mathematical Society, 31 (1929), 793–806;CrossRefGoogle Scholar also Kermack, and McCrea, , Proc. Edinburgh Math. Soc. (2), 2 (1931), 220–239.CrossRefGoogle ScholarKermack, and McCrea, used the relation obtained from (1) by placing c= - 1 .Google Scholar

page 119 note 1 Born, Heisenberg and Jordan, , ZS. f. Physik, 35 (1926), 563.CrossRefGoogle Scholar

page 120 note 1 Loe. cit., 224.Google Scholar

page 121 note 1 This result was obtained independently by the present author by this method prior to the publication of their paper.

page 125 note 1 Schwatt, I. J., Operations with Series (Univ. of Pennsylvania Press) (1924), chap. V.Google Scholar

page 125 note 2 Loc. cit., 227.Google Scholar