On periodic solutions to the Hamilton system associated with the Schrödinger operators with strongly nonlinear potentials

In this paper, we start from the periodic geodesic of generalized Hermite operators, and analyze their geometric characteristics and analytical properties. For the quantitative study of periodic solutions to the Schrödinger operators with non-polynomial potentials, we systematically discuss the corresponding Hamilton system, and use the harmonic balance method (HBM) and the modified harmonic balance method (mHBM) to approximate and estimate the periodic solution in high accuracy.