Solving two-mode squeezed harmonic oscillator and $k$th-order harmonic generation in Bargmann-Hilbert spaces

Abstract

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 $k\ge 3$, our result indicates that it does not have eigenfunctions and is thus ill-defined in the Bargmann-Hilbert space.

LaTex 13 pages, version to appear in J. Phys. A: Math. Theor

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