Alternative approaches to the description of quantum dynamics in multi-well potentials

TL;DR

This paper compares three methods for analyzing quantum dynamics in multi-well potentials, highlighting the advantages of supersymmetric quantum mechanics for incorporating multi-well features.

Contribution

It introduces and evaluates three approaches, emphasizing the effectiveness of supersymmetric quantum mechanics in modeling multi-well quantum systems.

Findings

Supersymmetric quantum mechanics provides a promising approach for multi-well potentials.

Spectral method effectively reconstructs spectra from time-dependent solutions.

Standard matrix diagonalization remains a fundamental technique.

Abstract

We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the spectral method, which allows to reconstruct the spectrum and stationary functions based on the time-dependent solution of the Schr\"odinger equation; iii) approximations with exact solutions obtained by the supersymmetric quantum mechanics technique. The latter approach proves to be the most promising as it gives a unique possibility to include the specific multi-well features of the problem directly in the calculation procedure.