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What is Hydrogen Atom Bound States in Parabolic Coordinates about?

This document summarizes the use of parabolic coordinates to describe the bound states of the hydrogen atom. It shows that the Hamiltonian commutes with both the angular momentum and the Runge-Lenz vector, generating a symmetry group isomorphic to SO(4). This allows obtaining the energy eigenvalues and eigenfunctions algebraically using ladder operators. The energy levels match the well-known expression for the hydrogen atom. The degeneracy of each level is n^2, where n is the principal quantum number.

Author

Veiko Castañeda

Language

EN