Geodesic
Free motion of $q$-deformed quantum particle
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 87-93 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers $q$ deformation of the Heisenberg algebra and a representation for it by finite-difference operators. It is shown that for the automorphism of the algebra corresponding to free motion there does not exist a polynomial Harniltonian generating it. The propertiesofplanewaves, i.e., the eigenfunctions of the $q$-deformed momentum operator, are also considered. It is noted that for $q=\exp(\pi i\vartheta)$, where $\vartheta$ is irrational, the eigenfunctions can be umneasurable. 
@article{TMF_1992_93_1_a6,
     author = {S. V. Kozyrev},
     title = {Free motion of $q$-deformed quantum particle},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--93},
     year = {1992},
     volume = {93},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/}
}
TY  - JOUR
AU  - S. V. Kozyrev
TI  - Free motion of $q$-deformed quantum particle
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 87
EP  - 93
VL  - 93
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/
LA  - ru
ID  - TMF_1992_93_1_a6
ER  - 
%0 Journal Article
%A S. V. Kozyrev
%T Free motion of $q$-deformed quantum particle
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 87-93
%V 93
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/
%G ru
%F TMF_1992_93_1_a6
S. V. Kozyrev. Free motion of $q$-deformed quantum particle. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 87-93. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a6/

[1] Arefeva I. Ya., Volovich I. V., Phys. Lett., 268 (1991), 179 | DOI | MR

[2] Biedenharn L. C., J. Phys. A, 22 (1989), L983 | DOI | MR

[3] Macfarlane A. J., J. Phys. A, 22 (1989), 4581 | DOI | MR | Zbl

[4] Damaskinskii E. B., Kulish P. P., Zap. nauchn. semin. LOMI, 189, 1990 | MR

[5] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR