Continued fractions and Schrödinger equations
Prof. Miloslav Znojil

Date, Time
04.12, 15:00 - 16:00

Affiliation
Nuclear Physics Institute CAS, 250 68 Rez, Czech Republic,
University of Hradec Králové, 50003 Hradec Králov, Czech Republic,
ISS, Durban University of Technology, 4000 Durban, South Africa,
SDSCT, Stellenbosch University, 7600 Stellenbosch, South Africa

Abstract
Bound or resonant quantum states are often treated as eigenstates of a non-Hermitian quantum Hamiltonian H, but the numerical localization of its real or complex energy eigenvalues is, in general, not easy. A reduced task is considered: We propose to compute just the real system-characterizing quantities called singular values of H. These values are specified as poles of the Pushnitski’s and Stampach’s Hermitized Greens function. Two forms of the representation of such a Green’s function are presented, both of them using the scalar or matrix continued fractions. For illustration, the idea is shown applicable to a family of multibosonic Bose-Hubbard-like complex Hamiltonians supporting both the real and complex energy eigenvalues. The recently popular transfer of the related mathematics to some other, non-quantum physical systems (like, typically, to the classical optics in paraxial approximation) will also be briefly mentioned.