Optimized basis expansion as an extremely accurate technique for solving time-independent Schr\"odinger equation

TL;DR

This paper introduces an optimized trigonometric basis method that achieves highly accurate solutions for the time-independent Schrödinger equation, including complex anharmonic oscillators, surpassing traditional approaches.

Contribution

The paper presents a novel optimized basis expansion technique that provides near-exact solutions for complex quantum systems not exactly solvable by standard methods.

Findings

High-accuracy energy eigenvalues obtained for anharmonic oscillators

Method outperforms traditional basis expansion techniques

Applicable to complex quantum systems with high precision

Abstract

We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic oscillator perturbed by a trigonometric anharmonic term as not exactly solvable cases and obtain the nearly exact solutions.