Geodesic
The $q$-deformed harmonic oscillator, coherent states, and the
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 315-322 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a $q$-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states {(}the last being defined as eigenstates of the annihilation operator{\rm)}. We calculate the product of the “coordinate–momentum” uncertainties in $q$-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals $1/2$, as in the standard quantum mechanics. For coherent states, the $q$-deformation results in a violation of the standard uncertainty relation{;} the product of the coordinate- and momentum-operator uncertainties is always less than $1/2$. States with the minimum uncertainty, which tends to zero, correspond to the values of $\lambda$ near the convergence radius of the $q$-exponential.
Mots-clés : $q$-deformation
Keywords: harmonic oscillator, creation operators, annihilation operators, coherent states, uncertainty relation. 
@article{TMF_2006_147_2_a7,
     author = {V. V. Eremin and A. A. Meldianov},
     title = {The $q$-deformed harmonic oscillator, coherent states, and the},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {315--322},
     year = {2006},
     volume = {147},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a7/}
}
TY  - JOUR
AU  - V. V. Eremin
AU  - A. A. Meldianov
TI  - The $q$-deformed harmonic oscillator, coherent states, and the
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 315
EP  - 322
VL  - 147
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a7/
LA  - ru
ID  - TMF_2006_147_2_a7
ER  - 
%0 Journal Article
%A V. V. Eremin
%A A. A. Meldianov
%T The $q$-deformed harmonic oscillator, coherent states, and the
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 315-322
%V 147
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a7/
%G ru
%F TMF_2006_147_2_a7
V. V. Eremin; A. A. Meldianov. The $q$-deformed harmonic oscillator, coherent states, and the. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 315-322. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a7/

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

[2] L. S. Biedenharn, J. Phys. A, 22 (1989), L873 | DOI | MR | Zbl

[3] P. P. Kulish, E. V. Damaskinsky, J. Phys. A, 23 (1990), L415 | DOI | MR | Zbl

[4] S. A. Alavi, S. Rouhani, Phys. Lett. A, 320 (2004), 327 | DOI | MR | Zbl

[5] M. R. Monteiro, L. M. C. S. Rodrigues, L. Wulck, Phys. Rev. Lett., 76 (1996), 1098 | DOI

[6] R. S. Johal, R. K. Gupta, Int. J. Mod. Phys. E, 7 (1998), 553 ; Z. Chang, H. Yan, Phys. Rev. A, 44 (1991), 7405 | DOI | MR | DOI

[7] D. Bonatsos, C. Daskaloyannis, P. Kolokotronis, J. Chem. Phys., 106 (1997), 605 ; M. Xie, X.-W. Hou, Z.-Q. Ma, Chem. Phys. Lett., 262 (1996), 1 | DOI | DOI

[8] S. Chaturvedi, V. Srinivasan, Phys. Rev. A, 44 (1991), 8020 | DOI | MR

[9] J. Zhang, Phys. Lett. B, 440 (1998), 66 | DOI | MR

[10] A. Lorek, A. Ruffing, J. Wess, Z. Phys. C, 74 (1997), 369 | DOI | MR

[11] J. Zhang, Phys. Lett. A, 262 (1999), 125 | DOI | MR | Zbl

[12] R. J. Finkelstein, Int. J. Mod. Phys. A, 13 (1998), 1795 | DOI | MR | Zbl

[13] R. Parthasarathy, R. Sridhar, Phys. Lett. A, 305 (2002), 105 | DOI | MR | Zbl

[14] R. J. Finkelstein, Lett. Math. Phys., 49 (1999), 105 | DOI | MR | Zbl

[15] X.-M. Liu, C. Quesne, Phys. Lett. A, 317 (2003), 210 ; J.-S. Wang, B.-Y. Wang, C.-Y. Sun, Phys. Lett. A, 246 (1998), 464 | DOI | MR | Zbl | DOI | MR | Zbl

[16] J. L. Gruver, Phys. Lett. A, 254 (1999), 1 | DOI | MR | Zbl

[17] A. Kempf, J. Math. Phys., 35 (1994), 4483 | DOI | MR | Zbl

[18] R. J. Glauber, Phys. Rev. Lett., 131 (1963), 2766 ; P. Carruthers, M. M. Nieto, Rev. Mod. Phys., 40 (1968), 411 | MR | DOI

[19] H. Maassen, H. van Leeuwen, J. Math. Phys., 36 (1995), 725 | DOI | MR | Zbl

[20] V. I. Man'ko, G. Marmo, S. Solimeno, F. Zaccaria, Phys. Lett. A, 176 (1993), 173 | DOI | MR