Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators
Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico
2 INIFTA, División Química Teórica, Blvd. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina
Accepted: 15 January 2021
Published online: 25 January 2021
We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation 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 one variable, the parameter in the Hamiltonian operator. As illustrative examples, we consider a particle 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021