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On Quantum Algebra

1926
7 pages
Published in:
  • Math.Proc.Cambridge Phil.Soc. 23 (2008) 4, 412-418,
  • Proc.Cambridge Phil.Soc. 23 (1926) 412-418
  • Published: Oct 24, 2008
DOI:
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Abstract: (Cambridge University Press)
For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra. These quantities are called q-numbers, and the numbers of ordinary mathematics c-numbers, while the word number alone is used to denote either a q-number or a c-number. Both q-numbers and c-numbers can occur together in the same piece of analysis, and even in the same equation, as numbers of the two kinds can be added together or multiplied. A c-number may, in fact, be regarded as a special case of the more general q-number. In the particular case when two numbers x; and y satisfy xy = yx, we shall say that x commutes with y. A c-number is assumed to commute with every number.