Finite-dimensional quantum mechanics of a particle |
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Authors: | R. Jagannathan T. S. Santhanam R. Vasudevan |
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Affiliation: | (1) Present address: Institute of Mathematical Sciences, Matscience,, 600 020 Madras, India;(2) Department of Electrical and Computer Engineering, University of New Hampshire, 03824 Durham, New Hampshire |
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Abstract: | This paper analyzes the possible implications of interpreting the finitedimensional representations of canonically conjugate quantum mechanical position, and momentum operators of a particle consistent with Weyl's form of Heisenberg's commutation relation as the actual position, and momentum operators of the particle when it is confined to move within a finite spatial domain, and regarding the application of current quantum mechanical formalism based on Heisenberg's relation to such a situation as an asymptotic approximation. In the resulting quantum mechanical formalism the discrete and finite position and momentum spectra of a particle depend on its rest mass and the spatial domain of confinement. Such a finite-dimensional quantum mechanics may be very suitable for describing the physics of particles confined to move within very small regions of space. |
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