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Physics LibreTexts

11.1 Schrodinger Spreadsheets

  • Page ID
    5685
  • [ "article:topic", "authorname:flowlerm" ]

    SCHRODINGER SPREADSHEETS

    Physics 751, 752  Michael Fowler, University of Virginia

    Fourier Series

    Square Well Spreadsheet

    Spherical Square Well Resonance Spreadsheet

    Simple Harmonic Oscillator Spreadsheet

    Some Spreadsheet Illustrations of Scattering Theory Concepts

    Phase Shifting by a Radial Square Well

    This illustrates how the phase shift from a radial square well (or barrier) behaves as a function of energy.

    (An animation of the diagrams on page 412 of Sakurai, for example.)

    Scattering Length for a Square Well or Barrier

    Extrapolates the zero-energy straight-line wavefunction outside the well to see how it intercepts the axis.

    (Page 415 of Sakurai.)

    A Resonant State inside a Radial Square Barrier

    Can be used to explore the relationship between resonances and bound states, and to see how the phase shift

    increases on passing through a resonance.

    A Square Well Resonance Generated by the Centrifugal Barrier

    A quantitative realization of the situation sketched on page 553 of Shankar. A square well can have a positive

    energy sharp resonance, provided the angular momentum is nonzero.

    Resonance Shape with Background Phase Shift

    A pole in the complex energy plane near the positive real axis gives a Lorentzian peak in the cross section,

    reaching the unitarity limit.  If there is a preexisting slowly varying background phase, there will be an energy

    at which the scattering cross section is zero, and for a substantial background phase, this will be close to the peak.

    In this spreadsheet, the background phase, set initially to zero, can be adjusted with the slidebar.