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Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing
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A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated

Matthew G Reuter1, Mark A Ratner, Tamar Seideman

  • 1Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, USA. mgreuter@u.northwestern.edu

The Journal of Chemical Physics
|September 11, 2009
PubMed
Summary

A new split-operator method efficiently solves the time-dependent Schrödinger equation using spherical harmonics. This technique easily handles azimuthal asymmetries and adaptive time steps, improving computational chemistry simulations.

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Area of Science:

  • Computational physics and chemistry
  • Quantum mechanics

Background:

  • Solving the time-dependent Schrödinger equation is crucial for understanding quantum systems.
  • Previous methods faced challenges with azimuthal asymmetries and computational efficiency.

Purpose of the Study:

  • To present an efficient split-operator technique for solving the time-dependent Schrödinger equation.
  • To address limitations of existing methods, particularly regarding azimuthal asymmetries and computational scaling.

Main Methods:

  • Developed a split-operator technique in an angular coordinate system.
  • Employed a fast spherical harmonics transform for efficient representation conversions.
  • Incorporated adaptive time stepping and addressed the "m-mixing" problem.

Main Results:

  • The method efficiently solves the time-dependent Schrödinger equation.
  • Facile inclusion of azimuthal asymmetries (m-mixing) is achieved.
  • The technique demonstrates favorable scaling and avoids explicit kinetic and potential energy matrix elements.

Conclusions:

  • The presented technique offers an efficient and versatile approach for quantum dynamics simulations.
  • This method advances the computational treatment of systems with azimuthal asymmetries.
  • The technique's favorable scaling and reduced computational demands facilitate complex quantum mechanical problem-solving.