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Hi, I'm trying to figure out the solution for the ground state of the hydrogen-atom, however it is not going well.
As far as i know, you can supress the angular dependence, because the states of hydrogen (or at least some of them) are spherically harmonic.
This way the schr. equation just reduces to a radial dependent equation, which has the solutions:
Ψ(r) = F(r)e^(-br), where b is a constant and F(r) a power series (the laguerre polynomials), which determines the number of the s-orbital such that if i just look at the ground state F(r) reduces to a constant. Now, am I right so far?
Well, if so, I'm finding it a little hard to determine these constant. I read somewhere, that you can do it using the normalization condition for the wave function, but isn't Ψ(r) also dependent on the other s-orbitals or how am I to solve the problem?
As far as i know, you can supress the angular dependence, because the states of hydrogen (or at least some of them) are spherically harmonic.
This way the schr. equation just reduces to a radial dependent equation, which has the solutions:
Ψ(r) = F(r)e^(-br), where b is a constant and F(r) a power series (the laguerre polynomials), which determines the number of the s-orbital such that if i just look at the ground state F(r) reduces to a constant. Now, am I right so far?
Well, if so, I'm finding it a little hard to determine these constant. I read somewhere, that you can do it using the normalization condition for the wave function, but isn't Ψ(r) also dependent on the other s-orbitals or how am I to solve the problem?