Exactly solvable Schrödinger eigenvalue problems for new anharmonic potentials with variable bumps and depths
School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, C1A 4P3, Canada
* e-mail: email@example.com
Accepted: 3 April 2020
Published online: 23 April 2020
A new approach based on Darboux transformations is introduced to generate classes of solvable Schrödinger equations for new anharmonic potentials with variable bumps and depths. By introducing the concept of a transformation key, we present a method of controlling the number of bumps and their depths in these potentials. Although this method was applied to the one-dimensional generalized harmonic oscillator potential, it can be easily adapted to generate exactly solvable potentials using other known quantum potentials.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020