  From a careful study of the transcendental equations fulfilled by the bound
state energies of a free particle in a quantum well, cylindrical wire or
spherical dot with finite potential barrier, we have derived analytical
expressions of these energies which reproduce impressively well the numerical
solutions of the corresponding transcendental equations for all confinement
sizes and potential barriers, without any adjustable parameter. These
expressions depend on a unique dimensionless parameter which contains the
barrier height and the sphere, wire or well radius.
