  We show that the phase-space formulation of general probabilistic theories
can be extended to include a generalized time-evolution and that it can
describe a nonquantum hydrogen-like system which is stable, has discrete energy
levels, and includes the Zeeman effect. This allows us to study dynamical
effects such as excitations of the hydrogen-like system by a resonant laser and
Rutherford scattering. Our construction demonstrates that classical theory and
quantum theory can be seen as specific choices of general probabilistic theory
in phase space and that other probabilistic theories also lead to measurable
predictions.
