Geodesic
Using the~evolution operator method to describe a~particle in a~homogeneous alternating field
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 364-380

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

Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass $M(t)$ and a nonrelativistic particle with a variable mass $M(t)$ in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.
Keywords: nonrelativistic particle, linear potential, evolution operator, coherent state, oscillatory state, Wigner function. 
@article{TMF_2018_194_2_a9,
     author = {Sh. M. Nagiyev},
     title = {Using the~evolution operator method to describe a~particle in a~homogeneous alternating field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {364--380},
     publisher = {mathdoc},
     volume = {194},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a9/}
}
TY  - JOUR
AU  - Sh. M. Nagiyev
TI  - Using the~evolution operator method to describe a~particle in a~homogeneous alternating field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 364
EP  - 380
VL  - 194
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a9/
LA  - ru
ID  - TMF_2018_194_2_a9
ER  - 
%0 Journal Article
%A Sh. M. Nagiyev
%T Using the~evolution operator method to describe a~particle in a~homogeneous alternating field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 364-380
%V 194
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a9/
%G ru
%F TMF_2018_194_2_a9
Sh. M. Nagiyev. Using the~evolution operator method to describe a~particle in a~homogeneous alternating field. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 364-380. http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a9/