Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 703–736 | Cite as

On Contact Interactions Realised as Friedrichs Systems

  • Marko ErcegEmail author
  • Alessandro Michelangeli


We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.


Abstract Friedrichs systems Point interaction Hamiltonians Grubb extension theory 

Mathematics Subject Classification

35F45 35Q40 81Q10 



We warmly thank N. Antonić and G. Dell’Antonio for enlightening discussions on the subject.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.SISSA Trieste – International School for Advanced StudiesTriesteItaly

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