Mona Lisa - ineffable smile of quantum mechanics

The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent mixture superposition, of cheerfulness and sadness. State of the physical system is among the most important concepts of quantum mechanics. Being the primitive concept of the theory, it is usually left undefined. However, by state we mean a list of some relevant characteristics of the system in question. More or less exact information about the quantities pertaining to the system are on this list, telling us how it is prepared. For operational reasons, state of the quantum mechanical system is represented by some vector of the Hilbert space. Precisely, rays represent states, while quantities are represented by the Hermitian operators acting in this Hilbert space of states. The spectral decomposition of the Hermitian operator, in the simplest possible case when the spectrum is discrete and nondegenerate, reads: