Nonrelativistic shifted-l expansion technique for three- and two-dimensional Schrodinger equation

TL;DR

This paper introduces the shifted-l expansion technique (SLET), a new method for calculating eigenvalues of the Schrödinger equation in 2D and 3D, which is more broadly applicable than previous methods.

Contribution

The paper develops and demonstrates the shifted-l expansion technique (SLET) for solving the Schrödinger equation in two and three dimensions, offering a more versatile approach than existing methods.

Findings

SLET effectively computes eigenvalues in 2D and 3D Schrödinger problems.

SLET is applicable to a wider range of physical problems than SLNT.

The method simplifies perturbation calculations using 1/ar{l} as a parameter.

Abstract

The shifted-l expansion technique (SLET) has been developed to get eigenvalues of Schrodinger equation in three (3D) and two dimensions (2D). SLET simply consists of 1/\bar{l} as a perturbation parameter, where \bar{l}=l-\beta, \beta is a suitable shift, l is the angular momentum quantum number for 3D-case, l=|m| for the 2D-case, and m is the magnetic quantum number. Unlike the shifted large-N expansion theory (SLNT), SLET seems to be applicable to a wider number of problems of significant interest in physics.