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Nov
22
comment Scattering states of Hydrogen atom in non-relativistic perturbation theory
You're right Arnold Neumaier, I made an unjustified jump. It does show explicitly the bound states are dense in $L^2(0, \infty)$. I've corrected the question.
Nov
22
revised Scattering states of Hydrogen atom in non-relativistic perturbation theory
Fixed incorrect description of reference
Nov
22
comment Scattering states of Hydrogen atom in non-relativistic perturbation theory
Thanks, that makes sense to me. The bound states are complete on the subspace of square integrable functions on $R^3 \setminus \{0\}$ with respect to the inner product $\langle\phi|\psi\rangle:=\int dx\phi(x)^*\psi(x)$ and the scattering states are the orthogonal complement of this subspace in the Hilbert space you mentioned. Though I'm surprised it's $\frac{dx}{|x|}$ and not $\frac{dx}{|x|^2}$.
Nov
22
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22
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Nov
22
revised Scattering states of Hydrogen atom in non-relativistic perturbation theory
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Nov
22
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Nov
22
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