  Using the formalism of extended N=4 supersymmetric quantum mechanics we
consider the procedure of the construction of multi-well potentials. We
demonstrate the form-invariance of Hamiltonians entering the supermultiplet,
using the presented relation for integrals, which contain fundamental
solutions. The possibility of partial N=4 supersymmetry breaking is determined.
We also obtain exact forms of multi-well potentials, both symmetric and
asymmetric, using the Hamiltonian of harmonic oscillator as initial. The
modification of the shape of potentials due to variation of parameters is also
discussed, as well as application of the obtained results to the study of
tunneling processes. We consider the case of exact, as well as partially broken
N=4 supersymmetry. The distinctive feature of obtained probability densities
and potentials is a parametric freedom, which allows to substantially modify
their shape. We obtain the expressions for probability densities under the
generalization of the Ornstein-Uhlenbeck process.
