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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Jagannathan, R., Santhanam, T.S. & Vasudevan, R. Finite-dimensional quantum mechanics of a particle. Int J Theor Phys 20, 755–773 (1981). https://doi.org/10.1007/BF00674253
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DOI: https://doi.org/10.1007/BF00674253