On the Connection Between Classical and Quantum Mechanics
|Title||On the Connection Between Classical and Quantum Mechanics|
|Keywords||quantum mechanics, relativistic formulae, velocity, light, mathematical, wave function|
In the hierarchy of physical theories classical Newton's mechanics may be considered as a "limit" of two more general theories: the relativistic classical mechanics and the non-relativistic quantum mechanics. In the first case, the limit is reached when in all relativistic formulae the velocity of light is going to infinity. The limiting procedure changes the shapes of formulae but does not change either the number of the physical interpretation of the corresponding quantities. In this sense we may say that we understand satisfactorily the limiting procedure both from the mathematical and physical point of view.
A similar conclusion is far to be true for the second case. All known ways of relating classical mechanics with "limits" of quantum mechanics suffer from the lack of precision. In particular, it is not known, either from mathematical or physical points of view, what is the classical limit of the most fundamental object of quantum mechanics - the wave function - when the Planck constant is going to zero.