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Based on 1) the spectral resolution of the energy operator; 2) the linearityof correspondence between physical observables and quantum Hermitian operators;3) the definition of conjugate coordinate-momentum variables in classicalmechanics; and 4) the fact that the physical point in phase space remainsunchanged under (canonical) transformations between one pair of conjugatevariables to another, we are able to show that <t_s|E_s>, the proper-timerest-energy transformation matrices, are given as a*exp[-iE_s t_s/\hbar], fromwhich we obtain the proper-time rest -energy evolution equationi\hbar{\partial/\partial t_s} |Psi>= \hat{E_s}|Psi>. For special relativisticsituations this equation can be reduced to the usual i\hbar{\partial/\partialt}|Psi>=\hat{E}|Psi> dynamical equations, where t is the "reference time" and Eis the total energy. Extension of these equations to accelerating frames isthen provided.

Derivation of the relativistic "proper-time" quantum evolution equations from Canonical Invariance