401 citations · 727 across the 45 of their papers we have counts for
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PT-symmetric eigenvalues for homogeneous potentials
Alexandre Eremenko, Andrei Gabrielov
We consider one-dimensional Schrödinger equations with homogeneous potential, under appropriate PT-symmetric boundary conditions. We prove the phenomenon which was discovered by Be…
Quasi-exactly solvable quartic: real algebraic spectral locus
Alexandre Eremenko, Andrei Gabrielov
We describe the real quasi-exactly solvable spectral locus of the PT-symmetric quartic using the Nevanlinna parametrization.
Two-parametric PT-symmetric quartic family
Alexandre Eremenko, Andrei Gabrielov
We describe a parametrization of the real spectral locus of the two-parametric family of PT-symmetric quartic oscillators. For this family, we find a parameter region where all eig…
Quasi-exactly solvable quartic: elementary integrals and asymptotics
Alexandre Eremenko, Andrei Gabrielov
We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an…
On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential
Per alexandersson, Andrei Gabrielov
In this paper, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schrödinger equation with quartic potentials. We…
Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families
Alexandre Eremenko, Andrei Gabrielov
In the first part of the paper, we discuss eigenvalue problems of the form -w"+Pw=Ew with complex potential P and zero boundary conditions at infinity on two rays in the complex pl…