Solvable Potentials from Supersymmetric Quantum Mechanics
Dong Sup Soh, Kyung Hyun Cho, Sang Pyo Kim
TL;DR
This paper explores a recurrence relation in supersymmetric quantum mechanics to discover new exactly solvable potentials and reproduce known shape-invariant potentials, advancing the understanding of solvable models in quantum physics.
Contribution
It introduces new classes of solvable potentials using Riccati-type differential equations and simple ans"atze, expanding the catalog of exactly solvable quantum models.
Findings
Found new classes of solvable potentials.
Reproduced known shape-invariant potentials.
Enhanced methods for identifying solvable quantum systems.
Abstract
A recurrence relation of Riccati-type differential equations known in supersymmetric quantum mechanics is investigated to find exactly solvable potentials. Taking some simple {\it ans\"atze}, we find new classes of solvable potentials as well as reproducing the known shape-invariant ones.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems · Nonlinear Waves and Solitons