Exactly-solvable quantum systems in terms of Lambert-W functions
A. Schulze-Halberg, A.M. Ishkhanyan
TL;DR
This paper introduces new exactly-solvable quantum models with potentials expressed via Lambert-W functions, including energy-dependent, supersymmetric, and two-dimensional Dirac systems, along with related mathematical formulas.
Contribution
It presents novel quantum systems solvable in closed form using Lambert-W functions, expanding the class of exactly-solvable models in quantum mechanics.
Findings
New Lambert-W based quantum potentials constructed
Derivation of Wronskian integral formulas for Lambert-W functions
Development of models with energy-dependent and supersymmetric potentials
Abstract
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger models using the supersymmetry formalism, and two-dimensional Dirac systems. In addition, we derive Wronskian integral formulas for Lambert-W functions.
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