Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,...)

A simple technique employed almost three decades ago to manufacture partial ly solvable quantum many-body problems is revisited. [A quantum problem is "partially solvable" if (only) some of its eigenvalues and eigenfunctions c an be exhibited]. The models thereby generated are characterized by Hamilto nians of normal form, i.e., standard kinetic plus momentum-independent pote ntial energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional sp ace; the examples focus on D=1, D=2, and D greater than or equal to 2, and include generalizations of, and additional results on, cases recently discu ssed in the literature, as well as new models. (C) 1999 American Institute of Physics. [S0022-2488(99)02409-3].