APS Logo

Schrödinger’s Original Quantum Mechanical Solution for Hydrogen

ORAL

Abstract

In 1926, Erwin Schr\"odinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schr\"odinger equation using the Laplace method, a powerful but rarely taught technique. This method lets one examine quantum mechanics from a complex-analysis perspective. This method is useful to consider when teaching quantum mechanics, as these techniques can be widely used, unlike the standard Frobenius method. No one has carefully gone through the arguments that Schr\"odinger used in this paper; instead it is often just stated that the solution was adopted from Schlesinger's famous differential equation textbook. In this talk, I introduce the Laplace method for solving differential equations and discuss how this method can be used to solve for the energy eigenfunctions of the hydrogen atom, following Schr\"odinger's original solution, with all the necessary details. This talk is based on work presented in a paper of the same name from Galler, Canfield, and Freericks, forthcoming in EJP.

–

Authors

  • Jeremy Canfield

    Georgetown University

  • Anuradha Gupta

    New Jersey Inst of Tech, Pennsylvania State University, Bard College, University of Mississippi, Drexel Univ, Collaborator, University of Dayton, Morgan State University, Louisiana State University, University of Geneva, Instituto Superior Tecnico - Lisboa, Department of Biochemistry and Molecular Biology, Rutgers University, Institute for Quantitative Biomedicine, Rutgers University, Pennsylvania State University, and University of Illinois at Urbana-Champaign, University of Illinois at Urbana-Champaign, Department of Chemical Engineering, New Jersey Institute of Technology, Department of Physics and Astronomy, Rutgers University-New Brunswick, Department of Physics, Rutgers University, Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany, Department of Physics and Fribourg Center for Nanomaterials, University of Fribourg, Chemin du Musée 3, CH-1700 Fribourg, Switzerland, The MacDiarmid Institute for Advanced Materials and Nanotechnology, 1010 Auckland, New Zealand, Department of Physics, College of William & Mary, Williamsburg, VA 23187-8795, USA, New Jersey Institute of Technology, Newark, NJ, USA, University of California, Los Angeles, CA, USA, University of California, Berkeley, CA, USA, Space Research Institute of RAS, Moscow, Russia, Georgetown University, Institut Polytechnique de Paris, University of Delaware, Brookhaven National Laboratory, San Diego State University, University of Chicago, University of Illinois at Chicago, Argonne National Laboratory, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA, University of Washington

  • Anuradha Gupta

    New Jersey Inst of Tech, Pennsylvania State University, Bard College, University of Mississippi, Drexel Univ, Collaborator, University of Dayton, Morgan State University, Louisiana State University, University of Geneva, Instituto Superior Tecnico - Lisboa, Department of Biochemistry and Molecular Biology, Rutgers University, Institute for Quantitative Biomedicine, Rutgers University, Pennsylvania State University, and University of Illinois at Urbana-Champaign, University of Illinois at Urbana-Champaign, Department of Chemical Engineering, New Jersey Institute of Technology, Department of Physics and Astronomy, Rutgers University-New Brunswick, Department of Physics, Rutgers University, Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany, Department of Physics and Fribourg Center for Nanomaterials, University of Fribourg, Chemin du Musée 3, CH-1700 Fribourg, Switzerland, The MacDiarmid Institute for Advanced Materials and Nanotechnology, 1010 Auckland, New Zealand, Department of Physics, College of William & Mary, Williamsburg, VA 23187-8795, USA, New Jersey Institute of Technology, Newark, NJ, USA, University of California, Los Angeles, CA, USA, University of California, Berkeley, CA, USA, Space Research Institute of RAS, Moscow, Russia, Georgetown University, Institut Polytechnique de Paris, University of Delaware, Brookhaven National Laboratory, San Diego State University, University of Chicago, University of Illinois at Chicago, Argonne National Laboratory, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA, University of Washington