Using the Feynman-Kac Path Integral Method in Finding Excited States of Helium.

ORAL

Abstract

Group theory considerations and properties of a continuous path are used to define a failure tree procedure for finding eigenvalues of the Schrodinger equation using stochastic methods. The procedure is used to calculate the lowest excited state eigenvalues of eigenfunctions possessing anti-symmetric nodal regions in configuration space using the Feynman-Kac path integral method. Within this method the solution of the imaginary time Schrodinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation and are found by identifying the eigenvalues for the irreducible representation corresponding to symmetric or antisymmetric eigenfunctions for each group operator. The method provides exact eigenvalues of excited states in the limit of infinitesimal step size and infinite time. The numerical method is applied to compute the eigenvalues of the lowest excited states of the helium atom that transform according to specific irreducible representations associated with explicitly determined symmetry groups.

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Authors

  • N.G. Fazleev

  • James M. Rejcek

  • Dana Dunn

    University of Texas at Arlington, Peoples Friendship University of the Russia, TSAAPT Officer, University of Texas at El Paso, Department of Chemistry, Stephen F. Austin University, Department of Physics, Stephen F. Austin University, Highland Park High School, Dallas, Texas, Lamar High School, Arlington, Texas, Angelo State University, Abilene Christian University, Southern Nazarene University, Texas Tech University, Sam Houston State University, University of Texas at Austin, Cornell University, University of Houston, University of Texas Center for Relativity, Ion Beam Modification and Analysis Laboratory (IBMAL), University of North Texas, University of North Texas, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, NanoTech Institute, University of Texas at Dallas, Richardson, TX 75083, Department of Physics, The University of Texas at Arlington, Arlington, Texas 76019, Department of Physics, University of Texas at Arlington, Arlington, TX, 76019, UTA High Energy Physics Group, Univ. of Texas, Arlington, USA, KAERI Korea, Changwon National Univ., Korea, Rutgers University, Iowa State University, Rigaku/MSC, Texas Christian University, Dept. of Physics, Changwon National University, Department of Physics, University of North Texas, Department of Chemistry and Biochemistry, Arizona State University, Research Center, Philip Morris USA, Harrington Department Bioengineering Arizona State University, Universidad Autonoma de Colima, Universidad de Buenos Aires, Department of Physics, University of Texas, Arlington, Chair, Department of Physics, University of Texas at Arlington, Dean of Science, University of Texas at Arlington, President, University of Texas at Arlington, Department of Electrical Engineering, Princeton University, Department of Physics, Texas A\&M University, NanoFAB Center and Electrical Engineering Department, University of Texas at Arlington, University of Texas at San Antonio, SEMATECH, University of Texas at Dallas, CINVESTAV Queretaro, Mexico and University of Texas at Dallas, Texas A\&M University, Departamento de F\'isica, FCEN, Universidad de Buenos Aires, Freescale Semiconductor, Inc., Department of Physics, UT Austin, Physics Department, The University of Texas at Arlington, Department of Physics, University of Texas at Arlington, Tolar High School, Granbury High School