A quantummechanical derivation of the eigenvalues of the quadratic Casimir operator of the algebra SU(n) in Young tableau representation

Abstract

The paper concerns the eigenvalues and eigenfunctions of the quadratic Casimir operator of the algebra SU(n) in the Young tableau representation. Our starting point is a concrete physical problem in second quantized formalism. We use quantummechanical and group theoretical vehicles to determine the aimed quantities. The tableaux are organized according to their eigenvalue. We also investigate the modification rules.