On two different kinds of resonances in one-dimensional quantum-mechanical models

TL;DR

This paper investigates two types of resonances in a one-dimensional quantum well with barriers, using Riccati-Padé and Rayleigh-Ritz methods, revealing different resonance behaviors and computational advantages of each approach.

Contribution

It compares the Riccati-Padé and Rayleigh-Ritz methods for identifying two resonance types in a quantum model, highlighting their respective capabilities.

Findings

Riccati-Padé method finds both resonance types as roots of Hankel determinants.

Rayleigh-Ritz method detects each resonance type within specific rotation angle intervals.

Both methods effectively analyze the resonance phenomena in the quantum well model.

Abstract

We apply the Riccati-Pad\'{e} method and the Rayleigh-Ritz method with complex rotation to the study of the resonances of a one-dimensional well with two barriers. The model exhibits two different kinds of resonances and we calculate them by means of both approaches. While the Rayleigh-Ritz method reveals each set at a particular interval of rotation angles the Riccati Pad\'{e} method yields both of them as roots of the same Hankel determinants.