On the two-dimensional stationary Schrödinger equation with a singular potential

DOI10.1016/J.JMAA.2010.11.004zbMath1210.35043OpenAlexW2092248418MaRDI QIDQ626191

Abdelhamid Meziani, Vladislav V. Kravchenko

Publication date: 22 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.11.004

zbMATH Keywords

Schrödinger equationgeneralized analytic functionpseudoanalytic functionsingular potentialVekua equation

Mathematics Subject Classification ID

Series solutions to PDEs (35C10) Schrödinger operator, Schrödinger equation (35J10) Other generalizations (nonlinear potential theory, etc.) (31C45) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items (2)

Singular generalized analytic functions ⋮ Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential

Cites Work

• Initial-boundary value problems for a class of homogeneous second-order elliptic systems on a plane with a singular point
• Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator
• Quantum deformation of the two-dimensional hydrogen atom in a magnetic field
• On the spectrum of two-dimensional Schrödinger operators with spherically symmetric, radially periodic magnetic fields
• On a transplant operator and explicit construction of Cauchy-type integral representations for \(p\)-analytic functions
• Singular anharmonicities and the analytic continued fractions
• An outline of the theory of pseudoanalytic functions
• Representation of solutions of a singular Cauchy–Riemann equation in the plane
• Applied Pseudoanalytic Function Theory
• Exact solutions to the Schrödinger equation for the potential in two dimensions
• Generalized CR Equation with a Punctual Singularity: The Model Case
• On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions
• An initial problem for a class of second-order elliptic systems in the plane with a singular point

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