Generalized Uncertainty Principle and angular momentum

Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems.