A phase that can appear in the wave function for a quantum-mechanical system that depends on various parameters when parallel transport is performed in parameter space, i.e. the set of all possible combinations of values for all the different parameters. The Berry phase is nonzero if the topology of the parameter space is nontrivial. The phase has many applications in physics and chemistry, including energy landscapes and the quantum Hall effect. The existence of the Berry phase was first pointed out by Sir Michael Berry (1941– ) in 1984.