Abstract
Based on (1) the spectral resolution of the energy operator; (2) the linearity of correspondence between physical observables and quantum self-adjoint operators; (3) the definition of conjugate coordinate–momentum variables in classical mechanics; and (4) the fact that the physical point in phase space remains unchanged under (canonical) transformations between one pair of conjugate variables to another, we are able to show that , the proper-time rest-energy transformation matrices, are given as aexp(−iEsts/ℏ), from which we obtain the proper-time rest-energy evolution equation . For special relativistic situations this equation can be reduced to the usual dynamical equations, where t is the ‘reference time’ and E is the total energy. Extension of these equations to accelerating frames is then provided.
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