[en] The generalized formulation for the probability distribution for scalar particle in general relativity is discussed. This is tested by the correspondence principle. In the high frequency short-wavelength limit it is shown that the generalized quantities exhibit correct physical properties. However, the formulation suffers a normalization problem. There, for example, a wave function might not be simultaneously normalizable in all reference frames. These conclusions are demonstrated in the Schwarzschild geometry, using suitable metrics, for: i) a stationary wave solution near the event horizon and ii) a general normalizable wave packet solution of the scalar field equation. It is also established the geodesic trajectory and the Heisenberg uncertainty principle for a wave packet in curved space time