  A flexible multi-parameter exactly solvable model of potential profile,
containing an arbitrary number of continuous smoothly shaped barriers and
wells, both equal or unequal, characterized by finite values and continuous
profiles of the potential and of its gradient, is presented. We demonstrate an
influence of both gradient and curvature of these potentials on the electron
transport and spectra of symmetric and asymmetric double-well (DW) potentials.
The use of this model is simplified due to one to one correspondence between
the algorithms of calculation of the transmittance of convex barriers and
energy spectra of concave wells. We have shown that the resonant contrast
between maximum and minimum in over-barrier reflectivity of curvilinear barrier
exceeds significantly the analogous effect for rectangular barrier with the
same height and width. Reflectionless tunneling of electrons below the bottom
of gradient nanostructures forming concave potential barriers is considered.
The analogy between dynamics of electrons in gradient fields and gradient
optics of heterogeneous photonic barriers is illustrated.
