Dimensional Scaling: Morphing Quantum into Classical Mechanics

Dudley Herschbach, Harvard University

The utility of dimensional scaling, interpolation, and perturbation methods is illustrated for some simple prototype problems that exemplify characteristic features: random walks, two-electron atoms, the H2+ and H2 molecules, the cluster integrals for virial coefficients of a hard sphere fluid, and recent applications to the correlation energy of Bose-Einstein condensates. These methods are capable of yielding high accuracy and also offer appealing heuristic perspectives, including aspects akin to the prequantum valence models of Neils Bohr, Gilbert Newton Lewis and Irving Langmuir and to the resonance motif of Linus Pauling.

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