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I am curious about the concept of bound state in the continuum. What is a simple example Hamiltonian which have this property and how can I derive this particular bound state?

What are the properties of this state?

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  • $\begingroup$ The hydrogen atom: en.wikipedia.org/wiki/Hydrogen-like_atom $\endgroup$ – Lorenz Mayer Feb 12 '19 at 11:50
  • $\begingroup$ In the hydrogen atom the bound states have negative energy while the scattering states (the continuum) have positive energies. These two regions of the spectrum seem separated. $\endgroup$ – Andrea Maiani Feb 12 '19 at 14:00
  • $\begingroup$ Ah, i understand. You want a system where the point spectrum is in the continuous spectrum. $\endgroup$ – Lorenz Mayer Feb 12 '19 at 14:06
  • $\begingroup$ I think this is the definition of a bound state in the continuum. But I am not an expert and I was only curious about that. $\endgroup$ – Andrea Maiani Feb 12 '19 at 14:29

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