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Quantum mechanics in finite dimensions

We explicitly compute, following the method of Weyl, the commutator [Q, P] of the position operatorQ and the momentum operatorP of a particle when the dimension of the space on which they act is finite with a discrete spectrum; and we show that in the limit of a continuous spectrum with the dimension going to infinity this reduces to the usual relation of Heisenberg.

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1. Matscience, Madras, India

   T. S. Santhanam

2. Physikalisches Institut der Universität Wurzburg, West Germany

   T. S. Santhanam

3. Matscience, Madras, India

   A. R. Tekumalla

1. T. S. Santhanam
2. A. R. Tekumalla

Santhanam, T.S., Tekumalla, A.R. Quantum mechanics in finite dimensions. Found Phys 6, 583–587 (1976). https://doi.org/10.1007/BF00715110

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• Received: 21 January 1975

• Issue Date: October 1976

• DOI: https://doi.org/10.1007/BF00715110

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