New applications of pseudoanalytic function theory to the Dirac equation

DOI10.1088/0305-4470/38/42/003zbMath1081.81031arXivmath-ph/0506072OpenAlexW3105719963MaRDI QIDQ5706151

Antonio Rafael Selva Castañeda, Vladislav V. Kravchenko

Publication date: 4 November 2005

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

Full work available at URL: https://arxiv.org/abs/math-ph/0506072

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Solutions to PDEs in closed form (35C05) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20)

Related Items (11)

On explicitly solvable Vekua equations and explicit solution of the stationary Schrödinger equation and of the equationdiv(σ∇u)=0 ⋮ On the quantum mechanics of bicomplex Hamiltonian system ⋮ Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients ⋮ Complete families of solutions for the Dirac equation using bicomplex function theory and transmutations ⋮ Transmutation operators and complete systems of solutions for the radial bicomplex Vekua equation ⋮ On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation ⋮ On Beltrami fields with nonconstant proportionality factor on the plane ⋮ On a transplant operator and explicit construction of Cauchy-type integral representations for \(p\)-analytic functions ⋮ Construction of transmutation operators and hyperbolic pseudoanalytic functions ⋮ Bicomplex Fibonacci quaternions ⋮ Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane

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