On the Fourier transform and the spectral properties of thep-adic momentum and Schrödinger operators

DOI10.1088/0305-4470/30/16/018zbMath0927.46060OpenAlexW2057955513MaRDI QIDQ4235345

Roberto Cianci, Andrei Yu. Khrennikov, Sergio A. Albeverio

Publication date: 6 December 1999

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/30/16/018

zbMATH Keywords

momentum operatormeasurementposition operatorp-adic quantum mechanicsp-adic Fourier transformp-adic Gaussian distribution

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Quantum measurement theory, state operations, state preparations (81P15) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (10)

Chaos in p-adic Statistical Lattice Models: Potts Model ⋮ Trace class operators and states in p-adic quantum mechanics ⋮ On topological extensions of Archimedean and non-Archimedean rings ⋮ On \(p\)-adic mathematical physics ⋮ \(p\)-adic valued quantization ⋮ Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures ⋮ Non-Archimedean normal operators ⋮ Summation of p-adic functional series in integer points ⋮ On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions ⋮ On descriptions of all translation invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three

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