A Note on Scattering in Deformed Space with Minimal Length
Department for Theoretical Physics, Ivan Franko National University of Lviv
12 Drahomanov St., Lviv, UA-79005, Ukraine
e-mail: mykola@ktf.franko.lviv.ua
Received:
Received: 23 March 2010; accepted 12 July 2010; published online: 20 September 2010
DOI: 10.12921/cmst.2010.16.02.195-199
OAI: oai:lib.psnc.pl:731
Abstract:
We consider the elastic scattering in deformed space with minimal length. We give the basic relation for the elastic scattering in deformed space. We also investigate the partial wave method in deformed space. It is shown that the relations for the scattering amplitude and cross-section formally coincides with ordinary ones
Key words:
References:
[1] D.J. Gross, P.F. Mende, String theory beyond the Planck scale. Nucl. Phys. B 303, 407-454 (1988).
[2] M. Maggiore, A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304, 65-69 (1993).
[3] E. Witten, Reflections on the Fate of Spacetime. Phys. Today 49, 24 (1996).
[4] A. Kempf, Uncertainty relation in quantum mechanics with quantum group symmetry. J. Math. Phys. 35, 4483-4496 (1994).
[5] A. Kempf, G. Mangano, R.B. Mann, Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108-1118 (1995).
[6] A. Kempf, On quantum field theory with nonzero minimal uncertainties in positions and momenta. J. Math. Phys. 38, 1347-1372 (1997).
[7] A. Kempf, Non-pointlike particles in harmonic oscillators. J. Phys. A 30, 2093-2101 (1997).
[8] H.S. Snyder, Quantized Space-Time. Phys. Rev. 71, 38-41 (1947).
[9] C. Quesne, V.M. Tkachuk, Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework. J. Phys. A 36, 10373-10389 (2003).
[10] C. Quesne, V.M. Tkachuk, More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum. J. Phys. A 37, 10095-10113 (2004).
[11] L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations. Phys. Rev. D 65, 125027 (8 pages) (2002).
[12] I. Dadić, L. Jonke, S. Meljanac, Harmonic oscillator with minimal length uncertainty relations and ladder operators. Phys. Rev. D 67, 087701 (4 pages) (2003).
[13] C. Quesne, V.M. Tkachuk, Dirac oscillator with nonzero minimal uncertainty in position. J. Phys. A 38, 1747-1765 (2005).
[14] T.V. Fityo, I.O. Vakarchuk, V.M. Tkachuk, One-dimensional Coulomb-like problem in deformed space with minimal lengt. J. Phys. A 39, 2143-2149 (2006).
[15] F. Brau, Minimal length uncertainty relation and the hydrogen atom. J. Phys. A 32, 7691-7696 (1999).
[16] S. Benczik, L.N. Chang, D. Minic, T. Takeuchi, Hydrogenatom spectrum under a minimal-length hypothesis. Phys. Rev. A 72, 012104 (4 pages) (2005).
[17] M.M. Stetsko, V.M. Tkachuk, Perturbation hydrogen-atom spectrum in deformed space with minimal length. Phys. Rev. A 74, 012101 (5 pages) (2006).
[18] M. M. Stetsko, Corrections to the ns levels of the hydrogen atom in deformed space with minimal length. Phys. Rev. A 74, 062105 (5 pages) (2006); M.M. Stetsko, Erratum: Corrections to the ns levels of the hydrogen atom in deformed space with minimal length. [Phys. Rev. A 74, 062105 (2006)], Phys. Rev. A 78, 029907 (1 page) (2008).
[19] M.M. Stetsko, V.M. Tkachuk, Scattering problem in deformed space with minimal length. Phys. Rev. A 76, 012707, (7 pages) (2007).
We consider the elastic scattering in deformed space with minimal length. We give the basic relation for the elastic scattering in deformed space. We also investigate the partial wave method in deformed space. It is shown that the relations for the scattering amplitude and cross-section formally coincides with ordinary ones
Key words:
References:
[1] D.J. Gross, P.F. Mende, String theory beyond the Planck scale. Nucl. Phys. B 303, 407-454 (1988).
[2] M. Maggiore, A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304, 65-69 (1993).
[3] E. Witten, Reflections on the Fate of Spacetime. Phys. Today 49, 24 (1996).
[4] A. Kempf, Uncertainty relation in quantum mechanics with quantum group symmetry. J. Math. Phys. 35, 4483-4496 (1994).
[5] A. Kempf, G. Mangano, R.B. Mann, Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108-1118 (1995).
[6] A. Kempf, On quantum field theory with nonzero minimal uncertainties in positions and momenta. J. Math. Phys. 38, 1347-1372 (1997).
[7] A. Kempf, Non-pointlike particles in harmonic oscillators. J. Phys. A 30, 2093-2101 (1997).
[8] H.S. Snyder, Quantized Space-Time. Phys. Rev. 71, 38-41 (1947).
[9] C. Quesne, V.M. Tkachuk, Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework. J. Phys. A 36, 10373-10389 (2003).
[10] C. Quesne, V.M. Tkachuk, More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum. J. Phys. A 37, 10095-10113 (2004).
[11] L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations. Phys. Rev. D 65, 125027 (8 pages) (2002).
[12] I. Dadić, L. Jonke, S. Meljanac, Harmonic oscillator with minimal length uncertainty relations and ladder operators. Phys. Rev. D 67, 087701 (4 pages) (2003).
[13] C. Quesne, V.M. Tkachuk, Dirac oscillator with nonzero minimal uncertainty in position. J. Phys. A 38, 1747-1765 (2005).
[14] T.V. Fityo, I.O. Vakarchuk, V.M. Tkachuk, One-dimensional Coulomb-like problem in deformed space with minimal lengt. J. Phys. A 39, 2143-2149 (2006).
[15] F. Brau, Minimal length uncertainty relation and the hydrogen atom. J. Phys. A 32, 7691-7696 (1999).
[16] S. Benczik, L.N. Chang, D. Minic, T. Takeuchi, Hydrogenatom spectrum under a minimal-length hypothesis. Phys. Rev. A 72, 012104 (4 pages) (2005).
[17] M.M. Stetsko, V.M. Tkachuk, Perturbation hydrogen-atom spectrum in deformed space with minimal length. Phys. Rev. A 74, 012101 (5 pages) (2006).
[18] M. M. Stetsko, Corrections to the ns levels of the hydrogen atom in deformed space with minimal length. Phys. Rev. A 74, 062105 (5 pages) (2006); M.M. Stetsko, Erratum: Corrections to the ns levels of the hydrogen atom in deformed space with minimal length. [Phys. Rev. A 74, 062105 (2006)], Phys. Rev. A 78, 029907 (1 page) (2008).
[19] M.M. Stetsko, V.M. Tkachuk, Scattering problem in deformed space with minimal length. Phys. Rev. A 76, 012707, (7 pages) (2007).
