We give a simple short derivation of the Clebsch-Gordan coefficients, motivated by simple introductory facts of\nquantum angular momentum. The derivation uses only binomial coefficients, eschewing raising- and loweringoperators,\ngroup theory, spinors and calculus.
The problem of angular momentum addition requires the calculation of Clebsch-Gordan coefficients. While systems involving small values of momenta and spin present no special problem, larger systems require extensive computational effort. This paper describes a straightforward method for computing the coefficients for any two-particle problem exactly by means of a simplified form of the recursion formula in a notation that is particularly accessible to the third- or fourth-year student. The method is summarized in a brief BASIC program.