Complete Analytic Solutions of the Mie-type Potentials in N-Dimensions

TL;DR

This paper derives exact analytical solutions for the N-dimensional Schrödinger equation with Mie-type potentials, including expectation values, virial theorem, and ladder operators, generalizing known 3D results.

Contribution

It provides a comprehensive analytical framework for solving Mie-type potentials in N-dimensions, extending previous 3D solutions and constructing ladder operators.

Findings

Exact solutions for N-dimensional Mie-type potentials obtained

Expectation values and virial theorem derived in N-dimensions

Ladder operators constructed for these potentials

Abstract

The exact solutions of the N-dimensional Schrodinger equation with the Mie-type potentials are obtained using the conventional Nikiforov-Uvarov method.The expectation values r^{-1} and r^{-2}$ and the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem.The ladder operators are also construct for the Mie-type potentials in N-dimensions and the matrix elements of some operators $r$ and r\frac{d}{dr} are analytically obtained from the ladder operators.And the general results reduce to the 3-dimensional case when N=3.