Collect. Czech. Chem. Commun. 2005, 70, 621-637

Quantum Mechanics Needs No Interpretation

Lubomír Skálaa,b,* and Vojtěch Kapsaa

a Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
b Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada


Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.

Keywords: Probability theory; Quantum mechanics; Classical mechanics; Schrödinger equation; Hamilton-Jacobi equation; Probability density current; Equations of motion.

References: 14 live references.