On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation

DOI10.1080/17476930701769058zbMath1151.30344arXiv0708.3649OpenAlexW2052156661MaRDI QIDQ3510044

Dominic Rochon

Publication date: 26 June 2008

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.3649

zbMATH Keywords

second-order elliptic operatorbicomplex numbershyperbolic numberspseudoanalytic functionscomplex Clifford algebrastwo-dimensional stationary Schrödinger equation

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Other generalizations of function theory of one complex variable (32A30) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20)

Related Items (13)

Multicomplex wave functions for linear and nonlinear Schrödinger equations ⋮ Multicomplex hyperfunctions ⋮ Fractional multicomplex polynomials ⋮ The Cauchy-Kowalewski product for bicomplex holomorphic functions ⋮ Bicomplex polyharmonicity and polyholomorphy ⋮ Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients ⋮ Complex Laplacian and derivatives of bicomplex functions ⋮ σ-monogenic functions in commutative algebras ⋮ The bicomplex dual fractional Hankel transform ⋮ Singularities of functions of one and several bicomplex variables ⋮ Bicomplex hyperfunctions ⋮ Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms ⋮ On Factorization of Bicomplex Meromorphic Functions

Cites Work

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• On a factorization of second-order elliptic operators and applications
• On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions
• New applications of pseudoanalytic function theory to the Dirac equation

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