  The commutators of the Poincar\'e group generators will be unchanged in form
if a unitary transformation relates the free generators to the generators of an
interacting relativistic theory. We test the concept of unitary transformations
of generators in the nonrelativistic case, requiring that the free and
interacting Hamiltonians be related by a unitary transformation. Other authors
have applied this concept to time-dependent perturbation theory to give
unitarity of the time evolution operator to each order in perturbation theory,
with results that show improvement over the standard perturbation theory. In
our case, a stationary perturbation theory can be constructed to find
approximate solutions of the radial Schr\"odinger equation for scattering from
a spherically symmetric potential. General formulae are obtained for the phase
shifts at first and second order in the coupling constant. We test the method
on a simple system with a known exact solution and find complete agreement
between our first- and second-order contributions to the s-wave phase shifts
and the corresponding expansion to second order of the exact solution.
