Abstract
An approximation previously proposed by Garrett to evaluate the en-
ergy level of a particle in a finite square well using the expression of the corresponding
level in an infinite one is extended to a spherical well. In this way, simple analytical
approximations are obtained for the energy levels of a particle in a spherical cavity with
penetrable walls, knowing the exact values of the corresponding levels in a similar cav-
ity, with impenetrable walls. The relative errors of this approximation are of order of
about 10−3. This approach can be extended to slightly deformed spherical dots (ellip-
soidal dots with a small eccentricity), with interesting applications in nanophysics and
nanotechnology.