Position Dependent Mass Approach and Quantization for a Torus Lagrangian

TL;DR

This paper introduces a novel approach combining position-dependent mass and quantization techniques to analyze a Lagrangian on a torus surface, transforming complex equations into solvable forms and obtaining exact solutions.

Contribution

It develops a new method linking position-dependent mass with quantization for torus Lagrangians, enabling transformation and exact solution of nonlinear equations.

Findings

Derived second order nonlinear differential equations from a torus Lagrangian.

Transformed equations into nonlinear quadratic and Mathews-Lakshmanan forms.

Obtained exact solutions through quantization of the transformed equations.

Abstract

We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position dependent mass approach developed by Mustafa for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and Mathews-Lakshmanan equations and found their exact solutions.