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Numerical Steepest Descent for Overlap Integrals of Semiclassical Wavepackets

by R. Bourquin and V. Gradinaru

(Report number 2015-12)

Abstract
In this report we show that classical Gauss quadrature is not adequate for a large class of correlation and overlap integrals originating from quantum mechanics. These integrals are usually highly oscillatory and therefore special methods are necessary for accurate computations. We develop and test a new, highly efficient method based on some recent results about numerical steepest descent to solve the problem stated. Our approach is built in principle to work for any number of space dimensions but some care must be taken not to run into the curse of dimensionality. Explicit formulae and algorithms are given in full generality.

Keywords: oscillatory integral, high dimensions, unbounded domain, numerical steepest descent, semiclassical wavepackets

@Techreport{BG15_602,
  author = {R. Bourquin and V. Gradinaru},
  title = {Numerical Steepest Descent for Overlap Integrals of Semiclassical Wavepackets},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-12.pdf },
  year = {2015}
}

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