  We analyze the two-mode squeezed harmonic oscillator and the $k$th-order
harmonic generation within the framework of Bargmann-Hilbert spaces of entire
functions. For the displaced, single-mode squeezed and two-mode squeezed
harmonic oscillators, we derive the exact, closed-form expressions for their
energies and wave functions. For the $k$th-order harmonic generation with
$k\geq 3$, our result indicates that it does not have eigenfunctions and is
thus ill-defined in the Bargmann-Hilbert space.
