Quantum mechanics of single molecules

Year, pages: 1997, 159 - 178

In traditional quantum mechanics, a density operator (non-pure state) cannot uniquely be decomposed into pure states and different decompositions are considered as being equivalent. Here it is argued that different decompositions of a thermal non-pure state sometimes refer to entirely different physical situations, as, for example, to molecules with or without nuclear structure. Among all the infinitely many different decompositions of a thermal state the most stable one (under external stochastic perturbations) is chosen. It is argued that this stable decomposition is uniquely determined by a maximum entropy principle in the sense of Jaynes.

This individual approach to quantum mechanics is checked for the quantum-mechanical Curie-Weiss model of a magnent. The question there is how “fast'' the specific magnetization gets a classical observable and how ”fast“ the superpositions of states with opposite permanent magnetization “die out” with increasing number $N$ of spins. This increasingly classical behaviour is described here by a large-deviation entropy, compatible with the usual limit $N\to∞$ of algebraic quantum mechanics. For finite $N$, the superposition principle is still universally valid and nevertheless an approximate classical observable ”magnetization“ appears, becoming strictly classical in the limit $N=∞$. It is argued that usual statistical (algebraic) quantum mechanics imposes too excessive conditions on symmetry breaking and classical structures (arising only in the limit of infinitely many degrees of freedom).

Amann, A. 1997. Quantum mechanics of single molecules. In Tatra Mountains Mathematical Publications, vol. 10, no.1, pp. 159-178. 1210-3195.

Amann, A. (1997). Quantum mechanics of single molecules. Tatra Mountains Mathematical Publications, 10(1), 159-178. 1210-3195.