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

A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is “partially solvable” if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on $\text{D=1,}$ $\text{D=2,}$ and $\text{D⩾2,}$ and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models.