Quasi-exactly solvable PT-symmetric sextic oscillators resulting from real quotient polynomials

Abstract

We present a method of constructing PT-symmetric sextic oscillators using quotient polynomials and show that the reality of the energy spectrum of the oscillators is directly related to the PT symmetry of the respective quotient polynomials. We then apply the method to derive sextic oscillators from real quotient polynomials and demonstrate that the set of resulting oscillators comprises a quasi-exactly solvable system that contains the real, quasi-exactly solvable sextic oscillator. In this framework, the classification of the PT-symmetric sextic oscillators on the basis of whether they result from real or complex quotient polynomials is a natural consequence.