2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93496The spectra and generalized eigenfunctions of the hyperbolic and parabolic generators of the standard representation of SU(1,1) in the one-mode boson Hilbert space are derived. The eigenfunctions are given in three different forms, corresponding to the coordinate, photon number, and Fock-Bargmann representations of the state vectors. The possible spectra of general second degree Hamiltonians are determined. Some corresponding results in the two-mode case are also given. - In the Appendix we prove completeness and orthonormality relations for the polynomials giving the number representation expansion coefficients of the generalized eigenfunctions of the hyperbolic generator (= squeezing generator). These polynomials are special cases of Pollaczek polynomials.This is a reproduction, with minor corrections and an added Appendix, of a paper published in J. Bertrand et al.(Eds.), Modern Group Theoretical Methods in Physics, Kluwer Academic Publishers 1995. 13 pQuantum Physicstext