Improving the One Dimensional Schr\"{o}dinger Equation

POSTER

Abstract

The simple harmonic oscillator (SHO) model is a useful approach for approximating energies close to the ground state in a one dimensional hydrogen atom. According to empirical evidence, the actual potential results in an asymmetric equilibrium point and exhibits and exhibits asymptotic behavior at large distances from the nucleus. This creates a problem in the SHO model, as it does not possess such characteristics, and as a result, has energy values that do not match do not agree with the known energy levels very well. We propose a new one dimensional potential that more accurately fits the empirical data than the SHO model. We test our model by comparing the Schr\"{o}dinger equation's energy states to accepted energy levels of the hydrogen atom. Possible other uses for this model include the description of energy levels of atoms other than the hydrogen atom.

Authors

  • Bradley Schorer

    Linfield College

  • Anthony Colaprete

    Triumf, Texas A\&M University, Tel Aviv University, TRIUMF, Simon Fraser University, Dept. of Physics, SFU, BC, Canada, Department of Physics and Astronomy, University of British Columbia, Cavendish Laboratory, University of Cambridge, Department of Physics, Simon Fraser University, University of British Columbia, University of Wisconsin-Madison, Brookhaven National Laboratory, Los Alamos National Laboratory, Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Korea, Department of Physics, Oregon State University, Corvallis, OR 97331-6507, Imago Scientific Instruments Corp., Department of Physics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6 Canada, Linfield College, PNNL, University of Washington, University of Victoria, IUPUI1, Wabash, IUPUI2, Environmental Biotechnology Institute, University of Idaho, Moscow ID 83843, Physics Department, University of Idaho, Moscow ID 83843, Environmental Biotechnology Institute, University of Idaho, Moscow, ID 83844, Physics Department, University of Idaho, Moscow, Idaho 83844, TRIUMF / UBC, 5CSNSM-IN2P3-CNRS, Universit\'e Paris 11, University of Manitoba, Texas A\&M, U. Manitoba, Tel Aviv U., U. British Columbia, Universidad de Pa\'is Vasco, Department of Physics, University of Idaho, Moscow, Idaho 83844-0903, University of Idaho, Boise State University, Idaho State University, NASA Ames Research Center

  • Anthony Colaprete

    Triumf, Texas A\&M University, Tel Aviv University, TRIUMF, Simon Fraser University, Dept. of Physics, SFU, BC, Canada, Department of Physics and Astronomy, University of British Columbia, Cavendish Laboratory, University of Cambridge, Department of Physics, Simon Fraser University, University of British Columbia, University of Wisconsin-Madison, Brookhaven National Laboratory, Los Alamos National Laboratory, Department of Molecular Science and Technology, Ajou University, Suwon 443-749, Korea, Department of Physics, Oregon State University, Corvallis, OR 97331-6507, Imago Scientific Instruments Corp., Department of Physics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6 Canada, Linfield College, PNNL, University of Washington, University of Victoria, IUPUI1, Wabash, IUPUI2, Environmental Biotechnology Institute, University of Idaho, Moscow ID 83843, Physics Department, University of Idaho, Moscow ID 83843, Environmental Biotechnology Institute, University of Idaho, Moscow, ID 83844, Physics Department, University of Idaho, Moscow, Idaho 83844, TRIUMF / UBC, 5CSNSM-IN2P3-CNRS, Universit\'e Paris 11, University of Manitoba, Texas A\&M, U. Manitoba, Tel Aviv U., U. British Columbia, Universidad de Pa\'is Vasco, Department of Physics, University of Idaho, Moscow, Idaho 83844-0903, University of Idaho, Boise State University, Idaho State University, NASA Ames Research Center