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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 1, 2005

Solutions of the Schrödinger equation for Dirac delta decorated linear potential

  • Haydar Uncu EMAIL logo , Hakan Erkol , Ersan Demiralp and Haluk Beker
From the journal Open Physics

Abstract

We have studied bound states of the Schrödinger equation for a linear potential together with any finite number (P) of Dirac delta functions. Forx where 0f; 0x 1x 2x P , theσ i are arbitrary real numbers, and the potential is infinite forx

Keywords: 03.65.Ge

[1] W. Greiner and B. Müller:Quantum Mechanics: Symmetries, 2nd revised Ed., Springer-Verlag, Berlin, 1994. 10.1007/978-3-642-57976-9Search in Google Scholar

[2] B. Govoreanu, P. Blomme, M. Rosmeulen, V.J. Houdt and K. De Meyer: “A model for tunneling current in multi-layer tunnel dielectrics”, Solid State Electronic, Vol. 47, (2003), pp. 1045–1053. http://dx.doi.org/10.1016/S0038-1101(02)00514-210.1016/S0038-1101(02)00514-2Search in Google Scholar

[3] P. Fendley: “Airy Functions in Thermodynamics Bethe Ansatz”Lett. Math. Phys. Vol. 49, (1999), pp. 229–233. http://dx.doi.org/10.1023/A:100765862210910.1023/A:1007658622109Search in Google Scholar

[4] J.Z. Imbrie: “Dimensional reduction and crossover to mean-field behavior for branched polymers”, Ann. Henri Poincare, Vol. 4, (2003), pp. 445–458. http://dx.doi.org/10.1007/s00023-003-0935-910.1007/s00023-003-0935-9Search in Google Scholar

[5] S. Flügge:Practical Quantum Mechanics, Springer, New York, 1974. Search in Google Scholar

[6] S. Alveberio, F. Gesztsy, P. Høegh-Krohn and H. Holden:Solvable Models in Quantum Mechanics, Springer, New York, 1988. 10.1007/978-3-642-88201-2Search in Google Scholar

[7] E. Demiralp and H. Beker: “Properties of bound states of the Schrödinger equation with attractive Dirac delta potentials”, J. Phys. A: Math. Gen., Vol. 36, (2003), pp. 7449–7459. http://dx.doi.org/10.1088/0305-4470/36/26/31510.1088/0305-4470/36/26/315Search in Google Scholar

[8] C. Cohen-Tannoudji, B. Diu and F. Laloë:Quantum Mechanics I, Hermann, Paris, 1977. Search in Google Scholar

[9] C. Kittel:Introduction to Solid State Physics, 7th Ed., John Wiley, New York, 1996. Search in Google Scholar

[10] T. Uchino and I. Tsutsui: “Supersymmetric quantum mechanics under point singularities”, J. Phys. A: Math. Gen., Vol. 36, (2003), pp. 6821–6846. http://dx.doi.org/10.1088/0305-4470/36/24/31810.1088/0305-4470/36/24/318Search in Google Scholar

[11] J.R. Barker: “The physics and fabrication of microstructures and microdevices”, In: M.S. Kelly and C. Weisbuch (Eds.):Proceedings in Physics, 13 Springer: New York, 1986, pp. 210–220. Search in Google Scholar

[12] W. Ellberfeld and M. Kleber:Zeitschrift für Physik B, Vol. 73, (1988), pp. 23–32. http://dx.doi.org/10.1007/BF0131215110.1007/BF01312151Search in Google Scholar

[13] G. Álvarez and B. Sundaram: “Perturbation theory for the Stark effect in a double δ quantum well”, J. Phys. A: Math. Gen., Vol. 37, (2004), pp. 9735–9748. http://dx.doi.org/10.1088/0305-4470/37/41/00910.1088/0305-4470/37/41/009Search in Google Scholar

[14] C. Weisbuch and B. Vinter:Quantum Semiconductor Structures: fundamentals and Applications, Academic Press, San Diego, 1991. 10.1016/B978-0-08-051557-1.50009-3Search in Google Scholar

[15] S.B. Monozon, V.M. Ivanov and P. Schmelcher: “Impurity center in a semiconductor quantum ring in the presence of a radial electric field”, Physical Review B, Vol. 70, (2004), pp. 205336–205347. http://dx.doi.org/10.1103/PhysRevB.70.20533610.1103/PhysRevB.70.205336Search in Google Scholar

Published Online: 2005-6-1
Published in Print: 2005-6-1

© 2005 Versita Warsaw

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