We evaluate the path of the free-falling point particle in an asymptotically flat spacetime. To review the observations of such observer we will define a localy flat spacetime by making use of the geodesics. The coresponding time-like and space-like vectors should be ? ? and ? ? respectively. Where ? is the proper time of the free-falling observer and ? is its space with cosideration that at any time this observer is simultaneous event. Hamiltonian is the time evolution of the wave equation which can be obtained from the Dirac equation. If Hamiltonian be hermition, operator of time evolution would be unitary. We need a definition for inner product in Hilbert space to verify the hermition of the hamiltonian. As this definition should be invariant under time transformation, we search for a conservative bilinear form. This conservative bilinear form is also derived from the Dirac equation. Finally, by making use of the definition of the inner product we will derive the hermition of the Hamiltonian and we shall see that this is equal to hamiltonian, so the hamiltonian is Hermitian. Keywords: Free-falling Observer, Geodesic, Localy Flat Spacetime, Hamiltonian, Time Evolution,