Supersymmetric partners of the trigonometric Poschl-Teller potentials
Alonso Contreras-Astorga, David J Fernandez C
TL;DR
This paper explores how supersymmetry transformations can generate new Hamiltonians from trigonometric Poschl-Teller potentials, allowing spectrum manipulation and boundary behavior analysis.
Contribution
It introduces methods to modify or preserve spectra of Poschl-Teller potentials using first and second-order supersymmetry transformations.
Findings
Spectrum can be selectively modified or left unchanged.
New potentials exhibit specific boundary behaviors.
Transformation techniques are fully characterized.
Abstract
The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Poschl-Teller potentials. The several possibilities of manipulating the initial spectrum are fully explored, and it is shown how to modify one or two levels, or even to leave the spectrum unaffected. The behavior of the new potentials at the boundaries of the domain is studied.
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