Rayleigh-Ritz variational method with suitable asymptotic behaviour

TL;DR

This paper presents an improved Rayleigh-Ritz variational method using nonorthogonal basis sets with correct asymptotic behavior, demonstrating faster convergence than existing orthogonal polynomial methods in one-dimensional double-well models.

Contribution

It introduces a novel basis set construction for variational calculations that enhances convergence speed over previous orthogonal polynomial approaches.

Findings

Faster convergence rate compared to orthogonal polynomial projection

Effective basis sets for one-dimensional models with correct asymptotics

Successful application to double-well oscillators

Abstract

We discuss Rayleigh-Ritz variational calculations with nonorthogonal basis sets that exhibit the correct asymptotic behaviour. We construct the suitable basis sets for general one-dimensional models and illustrate the application of the approach on two double-well oscillators proposed recently by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.