Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms

TL;DR

This paper investigates PT-symmetric complex quartic potentials with additional centrifugal and Coulombic terms, demonstrating the quasi-exact solvability of large multiplets of bound states with real energies through a finite secular equation.

Contribution

It introduces a method to obtain large multiplets of bound-state solutions with real energies for a complex quartic potential using a finite-dimensional secular equation.

Findings

Large multiplets of real-energy bound states are obtainable.

Quasi-exact solvability is achieved through a specific relationship between charges and energies.

The approach simplifies finding solutions to complex potentials.

Abstract

PT symmetric complex potential V(r) = - r^4 + i a r^3 + b r^2 + i c r + i d/r + e/r^2 is studied. Arbitrarily large multiplets of its closed bound-state solutions with real energies are shown obtainable quasi-exactly (i.e., with a certain relationship between their charges and energies) from a single underlying finite-dimensional secular equation.