Solving the Schr\"odinger Equation with Power Anharmonicity

TL;DR

This paper introduces a finite-rank approximation method to solve the Schrödinger equation for quantum anharmonic oscillators, providing approximate energy eigenvalues and analyzing convergence.

Contribution

The paper applies a nonstandard finite-rank approximation method to anharmonic oscillators, demonstrating its effectiveness in calculating energy levels.

Findings

Approximate energy eigenvalues obtained for anharmonic oscillators

Convergence behavior of the finite-rank approximation discussed

Method successfully applied to cubic and quartic anharmonicities

Abstract

We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a three-dimensional isotropic quantum anharmonic oscillator with additive cubic or quartic anharmonicity. Approximate energy eigenvalues are obtained and convergence of the method is discussed.