Multi-well potentials and extended supersymmetric quantum mechanics

TL;DR

This paper develops a method using extended N=4 supersymmetric quantum mechanics to construct and analyze multi-well potentials, including symmetric and asymmetric types, with applications to tunneling phenomena.

Contribution

It introduces a formalism for constructing multi-well potentials within extended supersymmetric quantum mechanics and explores partial supersymmetry breaking and potential modifications.

Findings

Derived exact multi-well potentials from harmonic oscillator Hamiltonian.

Demonstrated form-invariance of Hamiltonians in supermultiplets.

Discussed potential shape modifications and tunneling applications.

Abstract

Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the presented relation for integrals, which contain fundamental solutions. The possibility of partial $N=4$ supersymmetry breaking is determined. We also obtain exact forms of multi--well potentials, both symmetric and asymmetric, using the Hamiltonian of harmonic oscillator as initial. The modification of the shape of potentials due to variation of parameters is also discussed, as well as application of the obtained results to the study of tunneling processes.