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I've studied the HVZ theorem for the three body problem interacting with regular potentials. I'd like to extend this result to the three body problem with point interactions (delta potentials). Is there anyone who have studied this problem and knows some references about it?

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Few-Body Systems 38, 125 (2006): On critical stability of three quantum charges interacting through delta potentials, H.D. Cornean, P. Duclos, B. Ricaud.

We consider three one dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.

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  • $\begingroup$ Thank you for the link. I'm studying the problem in three dimension, but I'll surely read rour article. $\endgroup$ – Sue Mar 22 '13 at 15:47

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