  The dominantly orbital state method allows a semiclassical description of
quantum systems. At the origin, it was developed for two-body relativistic
systems. Here, the method is extended to treat two-body Hamiltonians and
systems with three identical particles, in $D\ge 2$ dimensions, with arbitrary
kinetic energy and potential. This method is very easy to implement and can be
used in a large variety of fields. Results are expected to be reliable for
large values of the orbital angular momentum and small radial excitations, but
information about the whole spectrum can also be obtained in some very specific
cases.
