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The approach of multi-dimensional SUSY Quantum Mechanics is used in anexplicit construction of exactly solvable 3-body (and quasi-exactly-solvable$N$-body) matrix problems on a line. From intertwining relations withtime-dependent operators, we build exactly solvable non-stationary scalar and$2\times 2$ matrix 3-body models which are time-dependent extensions of theCalogero model. Finally, we investigate the invariant operators associated tothese systems.Comment: 13 pages, LATE

Exactly solvable three-body systems with internal degrees of freedom