  Manipulating energy levels while controlling the electron localization is an
essential step for many applications of confined systems. In this paper we
demonstrate how to achieve electron localization and induce energy level
oscillation in one-dimensional quantum systems by externally controlling the
deformation of the system. From a practical point of view, the one-dimensional
potentials can be realized using layered structures. In the analysis, we
considered three different examples. The first one is a graded quantum well
between confining infinite walls where the deformation is modeled by varying
slightly the graded well. The second systems is a symmetric multiple quantum
well between infinite walls under the effect of biasing voltage. The third
system is a layered 2D hybrid perovskites where pressure is used to induce
deformation. The calculations are conducted both numerically and analytically
using the perturbation theory. It is shown that the obtained oscillations are
associated with level avoided crossings and that the deformation results in
changing the spatial localization of the electrons.
