We show that operators capable of converting certain spherical hydrogen atom eigenfunctions into others by raising the angular momentum quantum number ℓ can be constructed from components of the quantum mechanical Lenz vector operator. The derivation is performed using formalism no more sophisticated than that used to derive the properties of the angular momentum ladder operators in undergraduate quantum mechanics courses. The properties of these Lenz vector operators illustrate the accidental degeneracy of the hydrogen atom because they change the quantum number ℓ without affecting n.
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© 2004 American Association of Physics Teachers.
2004
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