Geodesic
Formulation of quantum mechanics with dynamical time
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 154-165

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

We consider quantum mechanics for which the system time is one of generalized coordinates. The generalized Hamiltonian has an unbounded spectrum, which allows us to introduce a Hermitian time operator. In the proposed formulation of quantum mechanics, a system time and observer's time are introduced. The Schrödinger equation in the system time either does not hold or holds only approximately. The wave function is assumed to be square integrable with respect to all coordinates, including the system time. In some limit, this formalism reproduces standard quantum mechanics and the corresponding measurement theory. 
@article{TM_2014_285_a10,
     author = {M. G. Ivanov},
     title = {Formulation of quantum mechanics with dynamical time},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {154--165},
     publisher = {mathdoc},
     volume = {285},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_285_a10/}
}
TY  - JOUR
AU  - M. G. Ivanov
TI  - Formulation of quantum mechanics with dynamical time
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2014
SP  - 154
EP  - 165
VL  - 285
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2014_285_a10/
LA  - ru
ID  - TM_2014_285_a10
ER  - 
%0 Journal Article
%A M. G. Ivanov
%T Formulation of quantum mechanics with dynamical time
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2014
%P 154-165
%V 285
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2014_285_a10/
%G ru
%F TM_2014_285_a10
M. G. Ivanov. Formulation of quantum mechanics with dynamical time. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 154-165. http://geodesic.mathdoc.fr/item/TM_2014_285_a10/