Time Evolution of Energy States

Abstract

In order to describe the time evolution of energy states we choose to abandon the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a more fundamental, relativistically correct Lagrangian method based on theories originally proposed by Dirac and Einstein. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, the function of the simplest quantum mechanical system an electron cyclotron, atomic clocks, matrix mechanics, chaos theory, and evolutionary biology.