Variational collocation for systems of coupled anharmonic oscillators

TL;DR

This paper introduces a variational collocation method to numerically solve the stationary Schrödinger equation for coupled anharmonic oscillators, optimizing convergence through parameter dependence and outperforming existing methods.

Contribution

It presents a novel collocation approach that leverages scale and angle parameters for improved accuracy in solving coupled oscillator systems.

Findings

Demonstrates faster convergence compared to traditional methods

Achieves high accuracy in energy eigenvalues

Validates approach through comparison with literature results

Abstract

We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.