
1. The Hydrogen Atom: Download
QM3D_2007.xls. Run QM3D, choosing the 'Coulomb' potential to simulate a hydrogen atom.
Verify that:

For a given angular momentum quantum number ℓ, the eigenenergies, in the units of this program, are given by E_{n} =1/n^{2}, where n is an integer larger than ℓ, and E_{n} is independent of ℓ. (For E = 1/2^{2}, type in "0.25", not "1/2^{2}".) The number of antinodes in the wavefunction is equal to n  ℓ. (Notice that this definition for n is different from the one you used last week.) NOTE: You may have to change the graph limits for large values of n. If so, double click on the chart axis, and treat it like any Excel chart.

Only angular momentum quantum numbers, ℓ, between 0 and n1 give valid wave functions. Verify this claim for all energy quantum numbers, n, less than or equal to 5.
