  The geometric potential in quantum mechanics has been attracted attention
recently, providing a formalism to investigate the influence of curvature in
the context of low-dimensional systems. In this paper, we study the
consequences of a helicoidal geometry in the Schr\"{o}dinger equation dealing
with an anisotropic mass tensor. In particular, we solve the problem of an
harmonic oscillator in this scenario. We determine the eigenfunctions in terms
of Confluent Heun Functions and compute the respective energy levels. The
system exhibit several different behaviors, depending on the adjustment on the
mass components.
