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The spectra and generalized eigenfunctions of the hyperbolic and parabolicgenerators of the standard representation of SU(1,1) in the one-mode bosonHilbert space are derived. The eigenfunctions are given in three differentforms, corresponding to the coordinate, photon number, and Fock-Bargmannrepresentations of the state vectors. The possible spectra of general seconddegree Hamiltonians are determined. Some corresponding results in the two-modecase are also given. - In the Appendix we prove completeness and orthonormalityrelations for the polynomials giving the number representation expansioncoefficients of the generalized eigenfunctions of the hyperbolic generator (=squeezing generator). These polynomials are special cases of Pollaczekpolynomials.

Spectra and Generalized Eigenfunctions of the One- and Two-Mode Squeezing Operators in Quantum Optics