1304.3979 (Yao-Zhong Zhang)

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

Yao-Zhong Zhang

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.

View original: http://arxiv.org/abs/1304.3979