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Through a semiquantal procedure, we study the perturbed modulation of amplitude and phase of Gross-Piteavskii equation describing trapped Bose–Einstein condensates in an optical lattice potential. By introducing quantum correctional parameters, the problem is quantized and leads to the derivation of a novel dynamical instability criterion. Additional degrees of freedom carrying quantum properties play a central role on the refine of the instability bandwidth, and, combined to the strength of optical lattice potential, entail unstable modes into full stability. A set of computational tools exhibited various features that bear instability characteristics, to confirm analytically predicted results. The quantum fluctuations thus have a stabilizing effect on the dynamics of harmonically trapped Bose–Einstein condensates in an optical lattice potential.

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