- #1
QuantumCosmo
- 29
- 0
Hi,
I was wondering if the bound solutions to the radial part of the hydrogen atom form a complete set for the functions in L^2(0,\infty). I know that the laguerre polynomials are complete and that they only differ from the radial solutions by factors of x^l * exp, so I thought that they would have to be complete too (apparently, it is not so simple as to say: "well, you are missing the scattering states, so of course they are not complete").
But I heard that it followed from Sturm-Liouville-Theory that they are not complete, which doesent seem to make any sense to me.
Does anyone have an idea?
Thank you,
QuantumCosmo
I was wondering if the bound solutions to the radial part of the hydrogen atom form a complete set for the functions in L^2(0,\infty). I know that the laguerre polynomials are complete and that they only differ from the radial solutions by factors of x^l * exp, so I thought that they would have to be complete too (apparently, it is not so simple as to say: "well, you are missing the scattering states, so of course they are not complete").
But I heard that it followed from Sturm-Liouville-Theory that they are not complete, which doesent seem to make any sense to me.
Does anyone have an idea?
Thank you,
QuantumCosmo