Using Genetic Programming To Solve the Schrodinger Equation

Created by W.Langdon from gp-bibliography.bib Revision:1.3872

  author =       "Dmitrii E. Makarov and Horia Metiu",
  title =        "Using Genetic Programming To Solve the Schrodinger
  journal =      "Journal of Physical Chemistry A",
  year =         "2000",
  volume =       "104",
  pages =        "8540--8545",
  keywords =     "genetic algorithms, genetic programming, DGP,
  ISSN =         "1089-5639",
  DOI =          "doi:10.1021/jp000695q",
  abstract =     "In a recent paper [Makarov, D. E.; Metiu, H. J. Chem.
                 Phys. 1998, 108, 590], \cite{makarov:1999:fpes:sfsdGP}
                 we developed a directed genetic programming approach
                 for finding the best functional form that fits the
                 energies provided by ab initio calculations. In this
                 paper, we use this approach to find the analytic
                 solutions of the time-independent Schrodinger equation.
                 This is achieved by inverting the Schrodinger equation
                 such that the potential is a functional depending on
                 the wave function and the energy. A genetic search is
                 then performed for the values of the energy and the
                 analytic form of the wave function that provide the
                 best fit of the given potential on a chosen grid. A
                 procedure for finding excited states is discussed. We
                 test our method for a one-dimensional anharmonic well,
                 a double well, and a two-dimensional anharmonic
  notes =        "

                 directed genetic programming (DGP), monte Carlo,
                 {"}straightforward GP...leads to poor results{"} p8451
                 DGP adds form of solution? Fset={+,-<*,/} pop=100
                 G<=250. Ekart well best(?) -1.5576eV, most within 0.5
                 percent. Even better with Bessel function. Also tried
                 Gaussian. NB {"}proper choice of the grid is
                 important{"} p852. Asymptotic region dominates
                 tunnelling. {"}we believe that...more readily find the
                 solution that has the simplest functional form{"} p8542
                 (ie the lowest energy eigenstate).

                 Excited states. Harmonic oscillator creation operator.
                 problems with second excited state? Hartree
                 approximation (p8544) , separate x and y dimensions,
                 use same bell curve for both x and y. x,y back
                 together? Seeded run? Fset now also includes exp First
                 excited state E=2.534.",

Genetic Programming entries for Dmitrii E Makarov Horia Metiu