Energy States of Electrons in Free Space

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the energy of an electron in free space = the continuous state.
The energy of an electron near the nucleus of an atom = the discontinuous state.

Are there other states? Is there a theory of states.
 
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The bound state energies of systems of particles correspond to poles in the green's function. There is in general a 'cutoff hyperbola' for which below the cutoff, the energy spectrum is discrete and composed of bound states and above the cutoff there is a continuous spectrum and free particle states. There is a fundamental difference when using the equation of QM/QFT to calculate interactions of systems of particles.

In regard to the radii of electron orbits around a nucleas, there is no limit to this radius so concepts like near or far do not really make sense. The answer is not difficult to obtain but to be concise would take a while. Would you like to do this?
 

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