BooksecrCollected Volumepp. 71–93

On the quantum mechanical three-body problem with zero-range interactions

  • Giulia Basti

    Università di Roma La Sapienza, Italy
  • Alessandro Teta

    Università di Roma La Sapienza, Italy
On the quantum mechanical three-body problem with zero-range interactions cover
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Abstract

In this note we discuss the quantum mechanical three-body problem with pairwise zero-range interactions in dimension three. We review the state of the art concerning the construction of the corresponding Hamiltonian as a self-adjoint operator in the bosonic and in the fermionic case. Exploiting a quadratic form method, we also prove self-adjointness and boundedness from below in the case of three identical bosons when the Hilbert space is suitably restricted, i.e., excluding the "s-wave“ subspace.