Independent eigenstates of angular momentum in a quantum N-body system - art. no. 042108

The global rotational degrees of freedom in the Schrodinger equation for an N-body system are completely separated from the internal ones. After remov ing the motion of the center of mass, we find a complete set of (2l + 1) in dependent base functions with angular momentum l. These are homogeneous pol ynomials in the components of the coordinate vectors and the solutions of t he Laplace equation, where the Euler angles do not appear explicitly. Any f unction with given angular momentum and given parity in the system can be e xpanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base func tions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the f unctions and in the equations. The permutation symmetry of the wave functio ns for identical particles is discussed.