Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective

We present and study a new class of Fock states underlying to discrete electromagnetic Schrödinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson–Charlier polynomials, Meixner polynomials, among other ones. The foundations of this work are...

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Veröffentlicht in:Applied mathematics and computation Jg. 315; S. 531 - 548
1. Verfasser: Faustino, N.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.12.2017
Schlagworte:
Clifford algebras
Fock states
Generalized Mittag-Leffler functions
Generalized Wright functions
Quasi-probability distributions
Generalized Wright functions
26A33
33C20
Quasi-probability distributions
30G35
Clifford algebras
Fock states
62F15
81Q60
Generalized Mittag-Leffler functions
ISSN:0096-3003, 1873-5649
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Beschreibung
Zusammenfassung:We present and study a new class of Fock states underlying to discrete electromagnetic Schrödinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson–Charlier polynomials, Meixner polynomials, among other ones. The foundations of this work are based on the exploitation of the quantum probability formulation ‘à la Dirac’ to the setting of Bayesian probabilities, on which the Fock states arise as discrete quasi-probability distributions carrying a set of independent and identically distributed (i.i.d) random variables. By employing Mellin–Barnes integrals in the complex plane we obtain counterparts for the well-known multidimensional Poisson and hypergeometric distributions, as well as quasi-probability distributions that may take negative or complex values on the lattice hZn.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.07.080