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I had a few questions about the most well behaved of atoms.

1) Solving the Schroedinger equation gives us a basis (say the energy eigenstates) such that all possible wavefunctions can be written as a linear combination of these stationery solutions. This means that the system is not confined to these stationery solutions but to their combinations, which are not necessarily eigenstates of the (time-independent) Hamiltonian.

Then why are the lines observed in the spectra are only those corresponding to transitions between the eigenstates labeled with (n,l,m,s)? Does the electron in a H atom only occupy these states as Bohr would have believed?

2)In a H atom, the energy depends only on n, not on l. Then why do we observe distinct lines for different l values of initial and final states?

3)The usual solution for the H atom is obtained by treating the nucleus as a classical point charge and utilising the classical Coulomb potential. Is it possible to obtain a completely quantum solution of the H atom? If so, what equations would be used?

Thanks for your help.

Molu