Abstract

One of the greatest achievements of physics in the century that is left behind is discovery of the existence of the quantum world, the world in which the traditional classical views are inapplicable. The theory was developed that is able to describe the events in this world, and it is called Quantum Theory. Despite its great achievements some of the most fundamental phenomena were left unexplained, which is mainly due to the yet unclear connection of the quantum world with the classical one. It will be shown in the lecture that in order to find this connection one should change emphases in classical theory. The traditional one is that a particle is represented as point in the phase space, while the correct representation is as the phase space (probability) density. This is result of inevitable uncertainties that one encounters in the measurement of position of particles in the phase space. Classical dynamics of particles is then formulated in terms of the phase space densities, and on a number of examples it will be shown what are the new features of this change of emphases. In the traditional classical mechanics there are no restrictions on the possible phase space (probability) densities, but by requiring that they obey the uncertainty principle, it will be shown, the dynamics (Schroedinger) equation of the quantum world is derived. The effect of tunneling will be discussed, on the basis of such formulation of classical mechanics, and it will be shown how it can be explained in terms of classical concepts.

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