We study new solvable few body problems consisting of generalizations of the Calogero and the Calogero–Marchioro–Wolfes three-body problems, by introducing non-translationally invariant three-body potentials. After separating the radial and angular variables by appropriate coordinate transformations, we provide eigensolutions of the Schrödinger equation with the corresponding energy spectrum. We found a domain of the coupling constant for which the irregular solutions are square integrable.
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 PACS: 02.30.Hq, 03.65.-w, 03.65.GeThe paper is organized as follows. In section 2 we expose and solve the problem for the linear case. The section 3 is devoted to extension to D-dimensional problem. Our conclusions are drawn in section 4.
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