Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

AMORE, PAOLO; FERNÁNDEZ, FRANCISCO M.

The European Physical Journal Plus

SPRINGER

Año: 2021 vol. 136

We calculate the exceptional points of the eigenvalues of several parameterdependent Hamiltonian operators of mathematical and physical interest. We show that thecalculation is greatly facilitated by the application of the discriminant to the secular determinant. In this way, the problem reduces to finding the roots of a polynomial function of just onevariable, the parameter in the Hamiltonian operator. As illustrative examples, we consider aparticle in a one-dimensional box with a polynomial potential, the periodic Mathieu equation,the Stark effect in a polar rigid rotor and in a polar symmetric top.