Energy-dependent harmonic oscillator in noncommutative space. (English) Zbl 1371.81177
Summary: In noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is studied by solving the Schrödinger equation in polar coordinates. The presence of the noncommutativity in space coordinates and the dependence on energy for the potential yield energy-dependent mass and potential. The correction of normalization condition is calculated and the parameter-dependences of the results are studied graphically.
MSC:
| 81R60 | Noncommutative geometry in quantum theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
References:
| [1] | Snyder, H. S., Phys. Rev.71, 38 (1947). · Zbl 0035.13101 |
| [2] | Seiberg, N. and Witten, E., JHEP09, 032 (1999). |
| [3] | Chaichian, M., Sheikh-Jabbari, M. M. and Tureanu, A., Phys. Rev. Lett.86, 2716 (2001). |
| [4] | Gamboa, J., Loewe, M. and Rojas, J. C., Phys. Rev. D64, 067901 (2001). |
| [5] | Wei, G.-F., Long, C.-Y., Long, Z.-W. and Qin, S.-J., Chin. Phys. C32, 247 (2008). |
| [6] | Mirza, B. and Mohadesi, M., Commun. Theor. Phys.42, 664 (2004). · Zbl 1167.81419 |
| [7] | Benzair, H., Merad, M., Boudjedaa, T. and Makhlouf, A., Z. Naturforsch.67a, 77 (2012). |
| [8] | Wang, J.-H., Li, K. and Sayipjamal, D., Chin. Phys. C32, 803 (2008). |
| [9] | Chetouani, L., Merad, M., Boudjedaa, T. and Lecheheb, A., Acta Phys. Slovaca55, 379 (2005). |
| [10] | Dulata, S. and Li, K., Chin. Phys. C32, 92 (2008). |
| [11] | Nair, V. P. and Polychronakos, A. P., Phys. Lett. B505, 267 (2001). · Zbl 0977.81046 |
| [12] | Gamboa, J., Loewe, M., Mendez, F. and Rojas, J. C., Mod. Phys. Lett. A16, 2075 (2001). · Zbl 1138.81384 |
| [13] | Falomir, H., Gamboa, J., Loewe, M., Mendez, F. and Rojas, J. C., Phys. Rev. D66, 045018 (2002). |
| [14] | Chaichian, M., Demichev, A., Presnajder, P., Sheikh-Jabbari, M. M. and Tureanu, A., Phys. Lett. B527, 149 (2002). · Zbl 1058.81510 |
| [15] | Lin, B.-S. and Heng, T.-H., Chin. Phys. Lett.28, 070303 (2011). |
| [16] | Jahan, A., Braz. J. Phys.38, 144 (2008). |
| [17] | Jing, J., Zhao, S., Chen, J. F. and Long, Z. W., Eur. Phys. J. C54, 685 (2008). · Zbl 1189.81113 |
| [18] | Pauli, W., Z. Phys.43, 601 (1927). · JFM 53.0858.02 |
| [19] | Sazdjan, H., Ann. Phys. (N. Y.)191, 52 (1989). · Zbl 0684.35086 |
| [20] | Lombard, R. J., Mareš, J. and Volpe, C., J. Phys. G: Nucl. Part. Phys.34, 1879 (2007). |
| [21] | Mollenauer, L. F., Stolen, R. H. and Gordon, J. P., Phys. Rev. Lett.45, 1095 (1980). |
| [22] | Formanek, J., Mares, J. and Lombard, R., Czech. J. Phys.54, 289 (2004). |
| [23] | Garcia-Martinez, J., Garcia-Ravelo, J., Pena, J. J. and Schulze-Halberg, A., Phys. Lett. A373, 3619 (2009). · Zbl 1233.81020 |
| [24] | Hassanabadi, H., Zarrinkamar, S. and Rajabi, A. A., Commun. Theor. Phys.55, 541 (2011). · Zbl 1264.81179 |
| [25] | Benchikha, A. and Chetouani, L., Mod. Phys. Lett. A28, 1350079 (2013). · Zbl 1268.81057 |
| [26] | Benchikha, A. and Chetouani, L., Cent. Eur. J. Phys.12, 392 (2014). |
| [27] | Le Bellac, M., Quantum Physics (Cambridge Univ. Press, 2006). · Zbl 1109.81002 |
| [28] | Grosche, C., J. Phys. A: Math. Gen.29, L183 (1996). · Zbl 0918.58014 |
| [29] | Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, eds. Jeffrey, A. and Zwillinger, D. (Academic Press, 2007). · Zbl 1208.65001 |
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