Computational Chemistry and Molecular Modeling
Atomic, Molecular and Optical Physics
Wiley InterScience Backfile Collection 1832-2000
Chemistry and Pharmacology
Equations of motion on the levels of classical mechanics, hydrodynamics, and wave mechanics are analyzed and existing connections are shown. The manifestation of particle and wave aspects on the different levels are investigated. Dissipative frictional forces are included and a nonlinear wave mechanical equation for these systems can be found. It follows the discussion of an alternative to the time-dependent Schrödinger equation (SE) in order to obtain the dynamical information on particle and wave aspects in a different form. This can be achieved by means of a Newtonian equation for a complex variable in connection with a conservation law for a nonclassical angular momentum-type quantity. With the help of this complex variable it is also possible to develop a Hamiltonian formalism for the wave aspect contained in the SE, the fluctuation, or uncertainty of position and momentum. In this case the Hamiltonian function is equivalent to the difference between the mean value of the Hamiltonian operator and the classical Hamiltonian function. Possible extensions and applications are mentioned.
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