Approximate solutions for N-body Hamiltonians with identical particles in D dimensions

A method based on the envelope theory is presented to compute approximate solutions for N-body Hamiltonians with identical particles in D dimensions (D ⩾ 2). In some favorable cases, the approximate eigenvalues can be analytically determined and can be lower or upper bounds. The accuracy of the method is tested with several examples, and an application to a N-body system with a minimal length is studied. Finally, a semiclassical interpretation is given for the generic formula of the eigenvalues.