Quasi-exact minus-quartic oscillators in strong-core regime

Abstract

PT-symmetric potentials $V({x}) = -{x}^4 +\j B {x}^3 + C {x}^2+\j D {x} +\j F/{x} +G/{x}^2$ are quasi-exactly solvable, i.e., a specific choice of a small $G=G^{(QES)}= integer/4$ is known to lead to wave functions $\psi^{(QES)}(x)$ in closed form at certain charges $F=F^{(QES)}$ and energies $E=E^{(QES)}$. The existence of an alternative, simpler and non-numerical version of such a construction is announced here in the new dynamical regime of very large $G^{(QES)} \to \infty$

Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators

“…For the solution, we employ the QES technique which is based on gauge transformation [53][54][55][56][57][58][59][60][61][62][63][64][65],…”

PT-symmetric, quasi-exactly solvable matrix Hamiltonians

“…In this section, referring to the unidimensional operator studied in [11] we will construct a P T -symmetric QES matrix Hamiltonian of the form…”

“…In section 4, we obtain a matrix generalization of the QES example of the P T -symmetric Hamiltonian with an anharmonic potential of degree four [8] and reconsidered recently [11]. Finally, in section 5, we show how the problem of section 4 can be transformed into a system of recurrence equations in the spirit of [12].…”