Computational aspects of the continuum quaternionic wave functions for hydrogen

DOI10.1016/J.AOP.2014.06.014zbMath1343.81247OpenAlexW2047845821MaRDI QIDQ305257

João Pedro Morais

Publication date: 29 August 2016

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aop.2014.06.014

zbMATH Keywords

Schrödinger equationquaternionic analysisassociated Laguerre polynomialFerrer's associated Legendre functionhydrogen continuum wave functionspherical monogenic

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) PDEs in connection with quantum mechanics (35Q40) Atomic physics (81V45) Applications of hypergeometric functions (33C90)

Related Items (7)

A modified uncertainty principle for two-sided quaternion Fourier transform ⋮ Constructing prolate spheroidal quaternion wave functions on the sphere ⋮ Controllability and observability of linear quaternion-valued systems ⋮ Conjugate harmonic functions of Fueter type ⋮ Ensemble control of linear systems with parameter uncertainties ⋮ Controllability and observability for linear quaternion-valued impulsive differential equations ⋮ Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation

Cites Work

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• Application of Sturmian functions to the Schrödinger three-body problem: Elastic \(e^ +\)-H scattering
• Real-part estimates for solutions of the Riesz system in ℝ³
• On Orthonormal Polynomial Solutions of the Riesz System in ℝ3
• On homogeneous polynomial solutions of the Riesz system and their harmonic potentials

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