Threshold conditions and bound states for locally periodic delta potentials

• Authors: Marappan Dharani , Basudeb Sahu , Chakrakodi Shastry
• Languages of publication: EN

Abstracts

EN

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g
n, n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D
1(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D
1(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D
1(N, g). A similar study is presented for case (b). Using the properties of D
1(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g
n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.

Keywords

EN

delta potential; bound states; scattering; threshold energy

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 10
• Pages: 755-766

Dates

published

1 - 10 - 2014

online

16 - 8 - 2014

Contributors

author

Marappan Dharani

• Department of Physics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore, 560035, India

author

Basudeb Sahu

• Department of Physics, North Orissa University, Baripada, 757003, India

author

Chakrakodi Shastry

• Department of Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India

References

• [1] C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996)
• [2] K. Gottfried, T.-M. Yan, Quantum Mechanics: Fundamental (Springer-Verlag, New York, 2003)
• [3] D.J. Griffiths, Introduction to Quantum mechanics (Pearson Education, New Jersey, 2005)
• [4] S.H. Patil, A.S. Roy, Physica A 253, 517 (1998) http://dx.doi.org/10.1016/S0378-4371(97)00644-4[Crossref]
• [5] B. Sahu, B. Sahu, Phys. Lett. A 373, 4033 (2009) http://dx.doi.org/10.1016/j.physleta.2009.09.018[Crossref]
• [6] E. Demiralp, H. Beker, J. Phys. A: Math. Gen. 36, 7449 (2003) http://dx.doi.org/10.1088/0305-4470/36/26/315[Crossref]
• [7] A.K. Jain, S.K. Deb, C.S. Shastry, Am. J. Phys. 46, 147 (1978) http://dx.doi.org/10.1119/1.11375[Crossref]
• [8] V. Bezák, J. Math. Phys. 37, 5939 (1996) http://dx.doi.org/10.1063/1.531758[Crossref]
• [9] A. Robinovitch, Am. J. Phys. 53, 768 (1985) http://dx.doi.org/10.1119/1.14310[Crossref]
• [10] C. Aslangul, Am. J. Phys. 63, 935 (1995) http://dx.doi.org/10.1119/1.18036[Crossref]
• [11] S. Geltman, J. At. Mol. Opt. Phys. 2011, 573179 (2011)
• [12] D. Witthaut, S. Mossmann, H.J. Korsch, J. Phys. A: Math. Gen. 38, 1777 (2005) http://dx.doi.org/10.1088/0305-4470/38/8/013[Crossref]
• [13] P.R. Berman, Am. J. Phys. 81, 190 (2013) http://dx.doi.org/10.1119/1.4769113[Crossref]
• [14] M. Dharani, B. Sahu, C.S. Shastry, Cent. Eur. J. Phys. 11, 995 (2013) http://dx.doi.org/10.2478/s11534-013-0259-4[Crossref]
• [15] D.J. Griffiths, C.A. Steinke, Am. J. Phys. 69, 137 (2001) http://dx.doi.org/10.1119/1.1308266[Crossref]
• [16] V. Bezak, J. Math. Phys. 48, 112108 (2007) http://dx.doi.org/10.1063/1.2806498[Crossref]
• [17] A.-C. Ji, W.M. Liu, J.L. Song, F. Zhou, Phys. Rev. Lett. 101, 010402 (2008) http://dx.doi.org/10.1103/PhysRevLett.101.010402[Crossref]
• [18] B. Li, X.-F. Zhang, Y.-Q. Li, Y. Chen, W.M. Liu, Phys. Rev. A. 78, 023608 (2008) http://dx.doi.org/10.1103/PhysRevA.78.023608[Crossref]
• [19] Z.X. Liang, Z.D. Zhang, W.M. Liu, Phys. Rev. Lett. 94, 050402 (2005) http://dx.doi.org/10.1103/PhysRevLett.94.050402[Crossref]
• [20] L.N. Pandey, T.F. George, Appl. Phys. Lett. 61, 1081 (1992) http://dx.doi.org/10.1063/1.107674[Crossref]
• [21] L.N. Pandey, T.F. George, M.L. Rustgi, J. Appl. Phys. 68, 1933 (1990) http://dx.doi.org/10.1063/1.346590[Crossref]
• [22] Y.-C. Chang, H. Yao, M. Mohiuddin, J. Appl. Phys. Lett. 75, 2686 (1999) http://dx.doi.org/10.1063/1.125118[Crossref]
• [23] W.C. Hsu, D. Guo, J. Appl. Phys. 73, 8615 (1993) http://dx.doi.org/10.1063/1.353392[Crossref]
• [24] J.M. Munoz-casteneda, J.M. Guilarte, A.M. Mosquera, Phys. Rev. D. 87, 105020 (2013) http://dx.doi.org/10.1103/PhysRevD.87.105020[Crossref]
• [25] W. Barford, M.W. Long, J. Phys. Condens. Matter 5, 199 (1993) http://dx.doi.org/10.1088/0953-8984/5/2/008[Crossref]

Identifiers

DOI

10.2478/s11534-014-0508-1