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Extending the four-body problem of Wolfes to non-translationally invariant interactions (1207.2933v3)
Published 12 Jul 2012 in math-ph and math.MP
Abstract: 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