2D H-atom in an arbitrary magnetic field via pseudoperturbation expansions through the quantum number l

TL;DR

This paper introduces the PSLET method to solve the 2D Schrödinger equation with cylindrically symmetric potentials, accurately reproducing known solutions and providing new eigenvalues for hybrid potentials.

Contribution

The paper presents a novel pseudoperturbative shifted-l expansion technique (PSLET) for solving the 2D Schrödinger equation with arbitrary cylindrically symmetric potentials.

Findings

Exact solutions for 2D Coulomb and harmonic oscillator potentials

Accurate eigenvalues for hybrid Coulomb-oscillator potentials

Validation against numerical solutions

Abstract

The pseudoperturbative shifted-l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrodinger equation with an arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduced. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.