High-Precision Value for the Quartic Anharmonic Oscillator Ground State

TL;DR

This paper presents a new algorithm combined with advanced multiplication techniques to compute the ground state of the quartic anharmonic oscillator with unprecedented precision exceeding 1000 digits.

Contribution

The paper introduces a simple yet highly effective algorithm that, together with FFT-based high-precision multiplication, achieves record-breaking accuracy in calculating the ground state.

Findings

Achieved ground state calculation with over 1000 digits of precision.

Demonstrated the efficiency of the new algorithm and multiplication method.

Set a new benchmark for precision in anharmonic oscillator computations.

Abstract

We will describe how a new, quite simple, but highly effective algorithm, together with the asymptotically fast FFT-based high-precision number multiplication of Mathematica 4 can calculate the ground state of the x^4 anharmonic oscillator to the new record of more than 1000 digits.