Physics 270

Problem 9: Schroedinger's Equation in "mixed media" 

  1. Introduction

    2. In the previous problem, you were able to find the energy eigenvalues of the Schroedinger Equation for a hydrogen atom using a spreadsheet. The accuracy of the calculation was poor, however. In this problem, we will put the calculation of the integrals into BASIC subroutines, in order to try to improve this accuracy.
    In order to make this work, you will have to develop a programming method to perform the actions that you did 'by hand' in the previous problem. Specifically, when the energy eigenvalue is not correct, the wavefunction diverges as you go to higher and higher radius. By looking at the way the wavefunction diverges, you can tell if you are 'high' or 'low' in eigenvalue. You now need to automate this process.
  2. Tasks
    1. Use the model spreadsheet provided, to set up the solution to the S.E. for a hydrogen atom. Your spreadsheet should allow you to change the desired precision (tolerance) on the energy eigenvalue, the spacing between steps in radius used in the integrations, and the range of radius used in the calculation.
    2. Write subroutines to calculate the S.E., by developing an algorithm for searching for the correct eigenvalue.
    3. Use your spreadsheet and subroutines to find the ground state and first excited state of the hydrogen atom. What step size is needed to get the eigenvalues correct to within 0.1 eV?