Chin. Phys. Lett.  2015, Vol. 32 Issue (07): 070301    DOI: 10.1088/0256-307X/32/7/070301
GENERAL |
Transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling
Diwaker**, Aniruddha Chakraborty
School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175005, India
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Diwaker, Aniruddha Chakraborty 2015 Chin. Phys. Lett. 32 070301
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Abstract The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.
Received: 08 April 2015      Published: 30 July 2015
PACS:  03.65.Nk (Scattering theory)  
  02.60.Cb (Numerical simulation; solution of equations)  
  03.65.Ge (Solutions of wave equations: bound states)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/32/7/070301       OR      https://cpl.iphy.ac.cn/Y2015/V32/I07/070301
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Diwaker
Aniruddha Chakraborty
[1] Datta K and Ranpal A 1981 Phys. Rev. D 23 2875
[2] Merzbacher E 1962 Quantum Mechanics (New York: Wiley)
[3] Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267
[4] Cramer J D and Nix J R 1970 Phys. Rev. C 2 1048
[5] Sharma R C and Leboeuf J N 1976 Phys. Rev. C 14 2340(R)
[6] Infeld L and Hull T E 1951 Rev. Mod. Phys. 23 21
[7] Barut A O, Inomata A and Wilson R 1987 J. Phys. A 20 4083
[8] Grosche C 1995 J. Phys. A: Math. Gen. 28 5889
[9] Hall R L and Saad N 1996 J. Phys. A: Math. Gen. 29 2127
[10] Dong S H and Sun G H 2003 Phys. Lett. A 314 261
[11] De R, Kronig L and Penney W G 1931 Proc. R. Soc. London A 130 499
[12] Kuhn H 1948 Helv. Chem. Acta 31 1441
[13] Tamm I 1932 Phys. Z. Sowjetunion. 1 733
[14] Seitz 1940 The Modern Theory of Solids (New York: Mc-Graw hill)
[15] Frost A A 1956 J. Chem. Phys. 25 1150
[16] Frost A A 1954 J. Chem. Phys. 22 1613
[17] Frost A A 1956 J. Chem. Phys. 25 1154
[18] Chakraborty A 2009 Mol. Phys. 107 165
[19] Baldo M and Ferreira L S 1999 Phys. Rev. C 59 682
[20] Chakraborty A 2009 Mol. Phys. 107 2459
[21] Song H Q, Baldo M, Giansiracusa G and Lombardo U 1998 Phys. Rev. Lett. 81 1584
[22] Chakraborty A 2011 Mol. Phys. 109 429
[23] Chakraborty A 2004 Ph. D. Dissertation (India: Indian Institute of Science)
[24] Chakraborty A 2010 Nano Devices 2D Electron Solvation and Curve Crossing Problems: Theoretical Model Investigations (Germany: Lambert Academic Publishing)
[25] Diwaker and Chakraborty A 2012 Mol. Phys. 110 2257
[26] Machleidt R, Holinde K and Elster C 1987 Phys. Rep. 149 1
[27] Diwaker and Chakraborty A 2012 Mol. Phys. 110 2197
[28] Diwaker and Chakraborty A 2015 Mol. Phys. (in press)
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