Keywordsquantum mechanics, many-body system, anyons, systems with minimal length, bound states
To obtain approximate analytical or numerical solutions of quantum N-body systems in D dimensions is an interesting but difficult problem. The situation is even more complicated for Hamiltonians with non-standard kinetic terms, such as systems with minimal length, or effective approaches in which the particles gain momentum-dependent mass. The auxiliary field method (AFM) provides approximate solutions to such problems in the case of N identical particles for D ≥ 2. In the most favourable cases, analytical bounds can be obtained.