Abstract
A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial potentials is constructed. These new Hamiltonians are different from the sextic QES Hamiltonians in the literature because their eigenfunctions obey PT-symmetric rather than Hermitian boundary conditions. These new Hamiltonians present a novel problem that is not encountered when the Hamiltonian is Hermitian: It is necessary to distinguish between the parametric region of unbroken PT symmetry, in which all of the eigenvalues are real, and the region of broken PT symmetry, in which some of the eigenvalues are complex. The precise location of the boundary between these two regions is determined numerically using extrapolation techniques and analytically using WKB analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
