Mathematics

We qualify the main features of the spectrum of the Hamiltonian of
point interaction for a three-dimensional quantum system consisting of three
point-like particles, two identical fermions, plus a third particle of different
species, with two-body interaction of zero range. For arbitrary magnitude of
the interaction, and arbitrary value of the mass parameter (the ratio between
the mass of the third particle and that of each fermion) above the stability
threshold, we identify the essential spectrum, localise and prove the finiteness
of the discrete spectrum, qualify the angular symmetry of the eigenfunctions,
and prove the monotonicity of the eigenvalues with respect to the mass parameter.
We also demonstrate the existence of bound states in a physically
relevant regime of masses.