  We construct a general algorithm generating the analytic eigenfunctions as
well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians.
Both exact and quasi-exact Hamiltonians enter our formalism but we focus on
quasi-exact interactions for which no such general approach has been considered
before. In particular we concentrate on a generalized sextic oscillator but
also on the Lame and the screened Coulomb potentials.
