*Infinite-Rydberg Limit of the Hydrogen Atom: The Lowest-Energy Unbound States*

Scientific Paper | |
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Title | Infinite-Rydberg Limit of the Hydrogen Atom: The Lowest-Energy Unbound States |

Read in full | Link to paper |

Author(s) | Michael H Brill |

Keywords | {{{keywords}}} |

Published | 2011 |

Journal | Proceedings of the NPA |

Volume | 8 |

No. of pages | 2 |

Pages | 84-86 |

**Read the full paper** here

## Abstract

The radial wavefunctions of the hydrogen atom have an interesting mathematical behavior in the limit of infinite *n*, which is the infinite Rydberg limit. Finding the limiting wavefunctions corresponds to solving the radial Schroedinger equation for *E* = 0. Frobenius expansion gives two solutions, each of which is a convergent expansion, but neither is square-integrable. For bound states, the second Frobenius solution is discarded because a relation between the solutions at *r* = 0 is violated and the square-integrable solution survives. We can't rule out either one of the *E* = 0 solutions solutions on the same grounds, which highlights the fact that half the mathematical solutions for the energies *E* < 0 have been artificially wiped away. We have lived without a probability interpretation for all the unbound-state wave functions, so I conjecture here that there may be physical significance to the non-integrable wave functions at *E* < 0 that are ignored in textbooks.