XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Oscar Rosas-Ortiz

Parity-time symmetry in supersymmetric quantum mechanics: An interplay between Riccati, Ermakov and Schrodinger equations

Nonlinear Riccati and Ermakov equations are combined to pair the energy
spectrum of two different quantum systems via the supersymmetric
approach. One of the systems is assumed Hermitian, exactly solvable,
with discrete energies in its spectrum. The other system is
characterized by a complex-valued potential that inherits all the
energies of the former one and includes an additional real eigenvalue in
its spectrum. The balanced gain and loss profile of such potential gives
rise to (but it is not restricted to) parity-time symmetry in
the supersymmetric quantum systems so constructed.

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of Bialystok
University of Bialystok

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