Nonlinear Oscillator Hamiltonian from Nonlinear Differential Equation and Calculation of Accurate Energy Levels

TL;DR

This paper introduces a novel approach to derive quantum Hamiltonians from nonlinear differential equations and accurately compute energy levels both analytically and numerically.

Contribution

It presents a new method for obtaining Hamiltonians from nonlinear equations and calculating energy levels with improved accuracy.

Findings

Analytical expressions for Hamiltonians derived from nonlinear differential equations.

Energy levels computed with high accuracy using both analytical and numerical methods.

Demonstrated effectiveness of the approach through comparison of results.

Abstract

A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using and numerically using matrix diagonalisation method.