On some signatures of Lie-Hamilton System in Quantum Hamilton Jacobi Equation

TL;DR

This paper explores the Lie-Hamilton structure of Quantum Hamilton Jacobi Equations for various mass models, revealing their reformulation as Cayley-Klein Riccati equations with symmetry properties.

Contribution

It demonstrates that Quantum Hamilton Jacobi Equations can be expressed as Cayley-Klein Riccati equations exhibiting Lie-Hamilton structure, including symmetry and integral expressions.

Findings

Equations can be recast as Cayley-Klein Riccati equations

Lie symmetry and Lie integral expressions are identified

Applicable to constant, position-dependent, and non-Hermitian mass models

Abstract

The general forms of Quantum Hamilton Jacobi Equation for a particle of constant mass, position dependent effective mass and non-Hermitian Effective mass Swanson model have been considered. It has been found that the said equations can be recast in the form of Cayley-Klein Riccati equations which admit a Lie-Hamilton structure. The possible expressions of Lie symmetry and Lie Integral have also been considered.