.(Note: r=10-6 is used instead of r=0 to prevent divide-by-zero errors.)
This spreadsheet is set up to solve the radial equation for u(r) and the
eigenvalues of H for a particle in a spherically symmetric potential.
The program
uses the Numerov method
to integrate the radial equation. All distance are measured in Å and all energies in eV.
The particle is assumed to be an electron. The program assumes that u(r)=0 at r=10Å.
It integrates inward towards the origin. The default potential is a square well potential
and l is assumed to be zero (s-state). The potential can easily be changed to any .
(Note: r=10-6 is used instead of r=0 to prevent
divide-by-zero errors.)
Instructions:
Run the macro to increment the trial energies in small steps. When u(0) changes
sign the program records an eigenvalue. When changing the potential, edit the macro and
change the starting value for the trial energies appropriately.
Only eigenvalues associated with radial functions, which rapidly decrease as r increases beyond a few Å, are physically reasonable solutions.