Physics – Quantum Physics
Scientific paper
2003-07-31
J. Phys. A: Math. Gen. 36 (2003) 9929-9941
Physics
Quantum Physics
18 pages plus 6 pages of appendices with new auxiliary identities
Scientific paper
10.1088/0305-4470/36/38/310
Three-body Schroedinger equation is studied in one dimension. Its two-body interactions are assumed composed of the long-range attraction (dominated by the L-th-power potential) in superposition with a short-range repulsion (dominated by the (-K)-th-power core) plus further subdominant power-law components if necessary. This unsolvable and non-separable generalization of Calogero model (which is a separable and solvable exception at L = K = 2) is presented in polar Jacobi coordinates. We derive a set of trigonometric identities for the potentials which generalizes the well known K=2 identity of Calogero to all integers. This enables us to write down the related partial differential Schroedinger equation in an amazingly compact form. As a consequence, we are able to show that all these models become separable and solvable in the limit of strong repulsion.
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