Exactly-solvable quantum systems in terms of Lambert-W functions

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 Schrödinger models with energy-dependent potentials, conventional Schrödinger models using the supersymmetry formalism, and two-dimensional Dirac systems. In addition, we derive Wronskian integral formulas for Lambert-W functions.

References in corpus (10)

• Supersymmetry and Quantum Mechanics
• Introduction to Dirac materials and topological insulators
• Wave equations with energy dependent potentials
• The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schrödinger form
• The Lambert-W step-potential - an exactly solvable confluent hypergeometric potential
• Wronskian differential formula for k-confluent SUSY QM
• Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation
• A globally diagonalizable alpha^2-dynamo operator, SUSY QM and the Dirac equation
• Resonances in the heavy symmetrical top with vibrating pivot
• Study of superradiance in the Lambert-W potential barrier