Can the mathematical formalism of quantum mechanics be applied to psychology?

We show that (in contrast to rather common opinion) the domain of applications of the mathematical formalism of quantum mechanics is not restricted to physics. This formalism can be applied to the description of various quantum-like (QL) information processing. In particular, the calculus of quantum (and more general QL) probabilities can be used to explain some paradoxical statistical data which was obtained in psychology and cognitive science. We consider the QL description of prisoners dilemma (PD) and so called disjunction effect (violation of Savage's sure thing principle which plays the fundamental role in modern economics).