2019
DOI: 10.48550/arxiv.1911.00452
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Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

Abstract: 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 p… Show more

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