Riccati nonhermiticity with application to the Morse potential

Solvable rational extensions of the Morse and Kepler-Coulomb potentials

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-Bäcklund transformations based on unphysical regular Riccati-Schrödinger functions which are obtained from specific symmetries associated to the considered family of potentials.

The Quantum Effective Mass Hamilton-Jacobi Problem

In this article, the quantum Hamilton- Jacobi theory based on the position dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Poschl- Teller potentials. The residue method is used to obtain the solutions of the quantum effective mass- Hamilton Jacobi equation. Further, it is shown that the eigenstates of the generalized non-Hermitian Swanson Hamiltonian for Morse and Poschl-Teller potentials can be obtained by using the Riccati equation without solving a differential equation.

Riccati、Ermakov 与 Schrödinger 方程之间的相互作用以产生具有实能谱的复值势

Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum

本文利用 Riccati 与 Ermakov 方程结合 Darboux 方法，构造能谱继承 Hermitian 可解系统全部能量且额外含一个实本征值且无奇点的复值势，并以 Morse 和三角 Pöschl-Teller 势为例说明。