Unbound states of the hydrogen atom

[Michael Cole]

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]

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.

Post by Michael Cole
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?

[Jos Bergervoet]

Post by Michael Cole
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"