Extending the four-body problem of Wolfes to non-translationally   invariant interactions
  We propose and solve exactly the Schr\"odinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type \cite{Wolf74} and additional non translationally invariant four-body potentials. We also generalize and solve exactly this problem in any $D$-dimensional space by providing full eigensolutions and the corresponding energy spectrum. We discuss the domain of the coupling constant where the irregular solutions becomes physically acceptable 
A. Bachkhaznadji and M. Lassaut
math-ph math.MP