Quantum dynamics within curved thin layers with the deviation

Abstract Combining the deviation between thin layers' adjacent surfaces with the confining potential method applied to the quantum curved systems, we derive the effective Schr$\ddot{o}$dinger equation describing the particle constrained within a curved layer, accompanied by a general geometric potential $V_{gq}$ composed of a compression-corrected geometric potential ${V_{gq}}^{\star}$ and a novel potential ${V_{gq}}^{\star\star}$ brought by the deviation. Applying this analysis to the cylindrical layer emerges two types of deviation-induced geometric potential, resulting from the the cases of slant deviation and tangent deviation, respectively, which strongly renormalizes the purely geometric potential and contribute to the energy spectrum based on a very substantial deepening of bound states they offer.