Using the Feynman-Kac Path Integral Method in Computing Eigenvalues and Matrix Elements for the Infinite Square Well with a Negative Delta Potential

ORAL

Abstract

The exact analytical solution of the Feynman-Kac path integral for the Infinite Square Well with a negative value delta function potential at the origin is presented and compared with numerical calculations approximated by random walk simulations on a discrete grid. In addition, a method using parity symmetry on the matrix element is presented that allows higher order eigenstates to be computed. The method provides exact values in the limit of infinitesimal step size and infinite time for the lowest eigenstates.

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Authors

  • Bruce Gnade

    Grand Valley State University, STC, Health Physics Society, The University of Texas at San Antonio, Texas Tech University, Lubbock, Texas, PIEAS, Pakistan, Texas Tech University, Lubbock, TX and PIEAS Pakistan, Rutgers University, Department of Physics, Texas A\&M University, College Station, TX 77843, Waxahachie Global High School, Waxahachie, TX, University of Texas at San Antonio, Tohoku University Institute of Materials Research, University of Alberta Department of Physics, Istanbul University Department of Physics, Geophysical Institute, Tohoku University, Japan, Planetary Plasma and Atmospheric Research Center, Tohoku University, Japan, Solar-Terrestrial Environment Laboratory, Nagoya University, Japan, Austin Community College, Dallas Baptist University, Angelo State University, Lake Highlands High School, Baylor University, Waco, TX, Texas Christian University, Fort Worth, TX, Paul Laurence Dunbar High School, Fort Worth, TX, Success High School, Fort Worth, TX, Dept. of Math., Univ. of New Mexico, Depts. of Materials Science and Engineering and Chemistry, University of Texas at Dallas

  • Nail G. Fazleev

    University of Texas at Arlington