CONTINUOUS-VARIABLE REPRESENTATION OF DYNAMIC GROUPS IN QUANTUM-SYSTEMS .2. THE EXTREME-EIGENSTATE APPROACH

The extreme-eigenstate approach to the solution of dynamic group repre sentation is formulated systematically based on the continuous represe ntation of the group generators and their intrinsic counterparts by vi rtue of two complete sets of commuting operators of first and second k inds (CSCO I and CSCO II). The high-order partial differential equatio ns for the general representation eigenstates in the conventional appr oach are replaced by a set of first-order partial differential equatio ns for the extreme eigenstate in this approach. This set of first-orde r partial differential equations is tractable for analytical solutions . By applying the ladder operators, any representation eigenstates can be obtained by standard differential operation. In application, the W iper SU(2) D function and the Elliott SU(3) irreducible representation basis are obtained by this approach as illustrations. The approach is proved to be simple, useful, and efficient for physicists.