Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Quasi-Exactly Solvable Sextic Polynomial Potentials   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.

30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics