  Particles moving on a radial ray with respect to a Schwarzschild mass are
shown to have SU(1,1)/U(1) dynamical symmetry. This symmetry is used to
identify a global time variable shared by all test particles moving on a radial
ray. With this time variable, Hamilton's equations for particles on a radial
ray have the form of the harmonic oscillator. The SU(1,1)/U(1) symmetry, in
conjunction with the well defined time variable and observer, assists in
determining the quantization of the motion of the test particles.
