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