Extending the Four-Body Problem of Wolfes to Non-Translationally Invariant Interactions

We propose and solve exactly the Schrödinger 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 [ 1 ] 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.