Discrete wave mechanics: Multidimensional systems.
Discrete wave mechanics is pursued further by extending the one-dimensional treatment to two (or more) dimensions in the light of explicit momentum considerations. Cognizance is taken of the effect of particle motion on mass and hence on the interactions between components of motion in different directions. The overall energy parameter turns out to be a product instead of a sum of parameters identified with each of several orthogonal axes. Accordingly, the separation of variables is most directly accomplished by factoring the principal energy parameter in conjunction with factoring the wave vector expression itself. Wave vector energies, on the other hand, remain additive. Finally, group velocity components are discussed for higher-dimensional systems.
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Department of Chemistry, B-017, University of California at San Diego, La Jolla, CA 92093.