Abstract
A quantum dynamical system is modeled by associating a complete set of orthogonal eigenfunctions labeled by position q (“pixels”), defined only at lattice points, plus other labelling indices (“colors”), and a complete set of orthogonal eigenfunctions labelled by momentum p, defined only inside the Brillouin zone, plus other corresponding labelling indices. Measurement of position q and momentum p are represented by operators \(\hat Q\) and \(\hat P\) multiplying the position (q) and momentum (p) eigenfunctions, respectively. The uncertainty relations for \(\hat Q\) and \(\hat P\) hold. We demonstrate that this model enable us to formulate quantum mechanics in a lattice, representing a reduced number of degrees of freedom.
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© 1989 Springer Science+Business Media Dordrecht
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Buot, F.A. (1989). Discrete Phase-Space Model for Quantum Mechanics. In: Kafatos, M. (eds) Bell’s Theorem, Quantum Theory and Conceptions of the Universe. Fundamental Theories of Physics, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0849-4_24
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DOI: https://doi.org/10.1007/978-94-017-0849-4_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4058-9
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