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Harris J. Silverstone
Johns Hopkins University Phone: 410.516.7431 PhD - California Institute of Technology Professor Silverstone is known for his work on expansions in quantum chemistry. The standard (Rayleigh-Schrödinger) perturbation theory for the energy levels of atoms in external electric and magnetic fields provides prime examples of expansions that diverge but are summable. Some are term-by-term real but have complex sums. Others are explicitly complex but have real sums. All these divergent expansions have associated with them exponentially small subseries that play a key role in their asymptotics. The exponentially small subseries are also important for "connection formulas" in semiclassical approximations of quantum mechanics. Professor Silverstone's recent work provides a detailed feature-by-feature analysis of the photoionization cross section of hydrogen in an electric field in terms of expansions over resonances. Extension to infinite fields leads to a complete understanding of the "Bender-Wu" branch cuts of the anharmonic oscillator, a somewhat serendipitous result. Earlier work used perturbation expansions to elucidate the transition between classical, semiclassical and quantum mechanics. Still earlier work concerned electron correlation (how electrons avoid each other) in atoms and molecules, the evaluation of molecular integrals using expansions generated from Fourier-transforms, and the use of piecewise-polynomial expansions for electronic wave functions. A separate research interest is the simulation of electron magnetic resonance spectra for high-spin iron in heme proteins and in enzymes. |
