TL;DR
This paper introduces supersymmetric quantum mechanics as a method for generating new solvable quantum potentials, analyzing algebraic structures, coherent states, and applications to periodic systems with band spectra.
Contribution
It presents general formulas for SUSY QM of first and second order in one dimension, with applications to trigonometric Pöschl-Teller and periodic potentials.
Findings
Generated new potentials with known spectra
Analyzed algebraic structures and coherent states
Applied techniques to periodic potentials with band spectra
Abstract
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Poschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.