These are illustrated for the hydrogen atom H, and are found by solving Eq. (12) with Maxima, an equation obtained from the lagrangian. This is a simpler method than the usual one, based on the hamiltonian. Eq. (12) can be transformed into a differential equation in phi and theta using the conic section in beta, Eq. (2), and the definition of beta, Eq. (4). That gives new angular wave functions for atoms and molecules.

a371stpapernotes7.pdf

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