Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design

TL;DR

This paper explores confluent second-order supersymmetric quantum mechanics to engineer Hamiltonians with tailored spectra, including adding, removing, or preserving energy levels, using hyperbolic Rosen-Morse and Eckart potentials.

Contribution

It introduces methods for spectral design in supersymmetric quantum mechanics with confluent second-order transformations applied to specific potentials.

Findings

Successfully generated Hamiltonians with modified spectra

Demonstrated spectral addition and deletion techniques

Analyzed isospectral transformation properties

Abstract

The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials. The possible spectral modifications, as to create a new level or to delete a given one, as well as the isospectral transformations, are discussed.