A nonlinear generalization of quantum mechanics for internal (spin) degrees of freedom has recently been developed by Weinberg [Phys. Rev. Lett. 62, 485 (1989); Ann. Phys. (N.Y.) 194, 336 (1989)]. We extend this theory to systems of composite, or multivalued, spin, such as atoms and molecules. Results for the generalized Hamiltonian function, energy eigenvalues, and state-vector time dependence are found to be similar for single- and multivalued spin systems, with the important difference that states of spin 0 or 1/2 can exhibit observable nonlinear behavior in a composite spin system. Examples of the application of the composite spin analysis are given for the ground-state hyperfine structure of the hydrogen and deuterium atoms.

• Received 20 February 1990

DOI:https://doi.org/10.1103/PhysRevA.42.63