  This paper presents the operator form of the effective potential V governing
the time evolution in 2 and 3 and n dimensional subspace of states. The general
formula for the n dimensional case is considered the starting point for the
calculation of the explicit formulae for 2 and 3 dimensional degenerate and
non-degenerate cases. We relate the 2 and 3 dimensional cases to some physical
systems which are currently investigated.
