The extreme-eigenstate approach to the solution of dynamic group representation is formulated systematically based on the continuous representation of the group generators and their intrinsic counterparts by virtue of two complete sets of commuting operators of first and second kinds (CSCO I and CSCO II). The high-order partial differential equations for the general representation eigenstates in the conventional approach are replaced by a set of first-order partial differential equations for the extreme eigenstate in this approach. This set of first-order 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 Wigner 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.

• Received 25 November 1992

DOI:https://doi.org/10.1103/PhysRevA.47.4641