Abstract.
The potential well and the step potential are studied under the modified Schrödinger equation due to minimal length in an exact analytical manner. The scattering problems as well as the reflection and transmission parameters are reported.
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K. Konishi, G. Paffuti, P. Provero, Phys. Lett. B 234, 276 (1990)
M. Maggiore, Phys. Lett. B 304, 65 (1993)
M. Maggiore, Phys. Rev. D 49, 5182 (1994)
M. Maggiore, Phys. Lett. B 319, 83 (1993)
L.J. Garay, Int. J. Mod. Phys. A 10, 145 (1995)
A. Kempf, G. Mangano, R.B. Mann, Phys. Rev. D 52, 1108 (1995)
F. Brau, J. Phys. A 32, 7691 (1999)
F. Scardigli, Phys. Lett. B 452, 39 (1999)
Y. Ran, L. Xue, S. Hu, R.-K. Su, J. Phys. A 33, 9265 (2000)
G. Amelino-Camelia, Phys. Lett. B 510, 255 (2001)
L.N. Chang, D. Minic, N. Okamura, T. Takeuchi, Phys. Rev. D 65, 125027 (2002)
F. Scardigli, R. Casadio, Class. Quantum Grav. 20, 3915 (2003)
J. Magueijo, L. Smolin, Phys. Rev. D 71, 026010 (2005)
J.L. Cortes, J. Gamboa, Phys. Rev. D 71, 065015 (2005)
J. Vahedi, Kourosh Nozari, P. Pedram, Gravit. Cosmol. 18, 211 (2012)
K. Nouicer, J. Math. Phys. 47, 122102 (2006)
M.V. Battisti, G. Montani, Phys. Lett. B 656, 96 (2007)
J. Slawny, J. Math. Phys. 48, 052108 (2007)
T.V. Fityo, I.O. Vakarchuk, V.M. Tkachuk, J. Phys. A: Math. Theor. 41, 045305 (2008)
C. Bambi, F.R. Urban, Class. Quantum Grav. 25, 095006 (2008)
S. Das, E.C. Vagenas, Phys. Rev. Lett. 101, 221301 (2008)
S. Das, E.C. Vagenas, Can. J. Phys. 87, 233 (2009)
S. Das, E.C. Vagenas, A.F. Ali, Phys. Lett. B 690, 407 (2010)
G.M. Hossain, V. Husain, S.S. Seahra, Class. Quantum Grav. 27, 165013 (2010)
D. Bouaziz, N. Ferkous, Phys. Rev. A 82, 022105 (2010)
A.F. Ali, S. Das, E.C. Vagenas, Phys. Rev. D 84, 044013 (2011)
H. Hassanabadi, S. Zarrinkamar, E. Maghsoodi, Phys. Lett. B 718, 678 (2012)
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Hassanabadi, H., Zarrinkamar, S. & Maghsoodi, E. Potential well and step potential within the framework of minimal length quantum mechanics. Eur. Phys. J. Plus 128, 138 (2013). https://doi.org/10.1140/epjp/i2013-13138-5
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DOI: https://doi.org/10.1140/epjp/i2013-13138-5