Geodesic
Quantum mechanics as the~quadratic Taylor approximation of classical mechanics: The~finite-dimensional case
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 278-291

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that in contrast to a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. We consider an approximation based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the second-order term. To escape technical difficulties related to the infinite dimensionality of the phase space for quantum mechanics, we consider finite-dimensional quantum mechanics. On one hand, this is a simple example with high pedagogical value. On the other hand, quantum information operates in a finite-dimensional state space. Therefore, our investigation can be considered a construction of a classical statistical model for quantum information.
Keywords: quantum average, classical average, approximation, small parameter, Taylor expansion.
Mots-clés : von Neumann trace formula 
@article{TMF_2007_152_2_a5,
     author = {A. Yu. Khrennikov},
     title = {Quantum mechanics as the~quadratic {Taylor} approximation of classical mechanics: {The~finite-dimensional} case},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {278--291},
     publisher = {mathdoc},
     volume = {152},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a5/}
}
TY  - JOUR
AU  - A. Yu. Khrennikov
TI  - Quantum mechanics as the~quadratic Taylor approximation of classical mechanics: The~finite-dimensional case
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 278
EP  - 291
VL  - 152
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a5/
LA  - ru
ID  - TMF_2007_152_2_a5
ER  - 
%0 Journal Article
%A A. Yu. Khrennikov
%T Quantum mechanics as the~quadratic Taylor approximation of classical mechanics: The~finite-dimensional case
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 278-291
%V 152
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a5/
%G ru
%F TMF_2007_152_2_a5
A. Yu. Khrennikov. Quantum mechanics as the~quadratic Taylor approximation of classical mechanics: The~finite-dimensional case. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 278-291. http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a5/