Solving the two-mode squeezed harmonic oscillator and the kth-order harmonic generation in Bargmann–Hilbert spaces

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