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

Abstract

Recently Zhang (2013 J. Phys. A: Math. Theor. 46 455302) proposed an analytical approach to solve the time-independent Schrödinger equation for the single-mode and two-mode squeezed harmonic oscillators in the Bargmann space of entire functions. In this comment we show that the eigenfunctions of these two systems exist in closed form and are expressed in terms of the Hermite polynomials. Moreover, since both oscillators exhibit the SU(1,1) dynamical symmetry, the eigenvalue problem can be tackled in a unified manner. In the Hilbert space of analytic functions of a complex variable in the unit disc, the energy eigenvalue equations involve first-order ordinary differential equations only, so we can easily solve these equations to obtain simple closed-form solutions.