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  • Unbound states of the hydrogen atom

    From Michael Cole@21:1/5 to All on Sun Apr 26 09:25:29 2020
    Hi all. Does anyone know where to find a good elegant mathematical
    treatment of the quantum hydrogen atom? The bound states are, of
    course, treated in every textbook, but they usually don't address the
    unbound states. I tried to tackle it myself as an exercise, but I am
    having trouble finding the right normalization of the continuous
    spectrum of unbound energy states. Is there a good reference for this?

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  • From Jos Bergervoet@21:1/5 to Michael Cole on Sun Apr 26 15:06:42 2020
    On 20/04/26 11:25 AM, Michael Cole wrote:
    Hi all. Does anyone know where to find a good elegant mathematical
    treatment of the quantum hydrogen atom? The bound states are, of
    course, treated in every textbook, but they usually don't address the
    unbound states. I tried to tackle it myself as an exercise, but I am
    having trouble finding the right normalization of the continuous
    spectrum of unbound energy states. Is there a good reference for this?

    These unbound states of course do not have a finite norm for the
    integrated wave function squared, but presumably you mean the
    normalization convention for the "Coulomb wave functions".

    The treatment in A&S handles that on page 538. See:
    http://people.math.sfu.ca/~cbm/aands/subj.htm
    "Coulomb wave functions ..... 509, 537"

    --
    Jos

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  • From Hendrik van Hees@21:1/5 to Michael Cole on Sun Apr 26 15:06:28 2020
    A very nice treatment of the full hydrogen problem is in

    J. J. Sakurai, Modern Quantum Mechanics, Addison Wesley

    using the standard wave-mechanical techniques.

    On 26/04/2020 11:25, Michael Cole wrote:
    Hi all. Does anyone know where to find a good elegant mathematical
    treatment of the quantum hydrogen atom? The bound states are, of
    course, treated in every textbook, but they usually don't address the
    unbound states. I tried to tackle it myself as an exercise, but I am
    having trouble finding the right normalization of the continuous
    spectrum of unbound energy states. Is there a good reference for this?


    --
    Hendrik van Hees
    Goethe University (Institute for Theoretical Physics)
    D-60438 Frankfurt am Main
    http://fias.uni-frankfurt.de/~hees/

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