Transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling

doi:10.1088/0256-307X/32/7/070301

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

Cite this article:

Diwaker, Aniruddha Chakraborty 2015 Chin. Phys. Lett. 32 070301

Download: PDF(591KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/32/7/070301 OR https://cpl.iphy.ac.cn/Y2015/V32/I07/070301

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	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)

Related articles from Frontiers Journals

[1]	Wenjie Miao, Zhiang Linghu, Qiujiao Du, Pai Peng, and Fengming Liu. Superscattering of Underwater Sound via Deep Learning Approach[J]. Chin. Phys. Lett., 2023, 40(1): 070301
[2]	Qianju Song, Shiwei Dai, Dezhuan Han, Z. Q. Zhang, C. T. Chan, and Jian Zi. PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum[J]. Chin. Phys. Lett., 2021, 38(8): 070301
[3]	L. Jin and Z. Song. Symmetry-Protected Scattering in Non-Hermitian Linear Systems[J]. Chin. Phys. Lett., 2021, 38(2): 070301
[4]	Shifeng Yang, Tianwei Zhou, Chen Li, Kaixiang Yang, Yueyang Zhai, Xuguang Yue, Xuzong Chen. Superfluid-Mott-Insulator Transition in an Optical Lattice with Adjustable Ensemble-Averaged Filling Factors[J]. Chin. Phys. Lett., 2020, 37(4): 070301
[5]	Shi-Feng Yang, Zi-Tong Xu, Kai Wang, Xiu-Fei Li, Yue-Yang Zhai, Xu-Zong Chen. A Quasi-1D Potential for Bose Gas Phase Fluctuations[J]. Chin. Phys. Lett., 2019, 36(8): 070301
[6]	ZHU Jun-Yi, GENG Xian-Guo. The ?-Dressing Method for the Sasa–Satsuma Equation with Self-Consistent Sources[J]. Chin. Phys. Lett., 2013, 30(8): 070301
[7]	LI Zhi, WANG Jian-Zhong, FU Li-Bin. Double Barrier Resonant Tunneling in Spin-Orbit Coupled Bose–Einstein Condensates[J]. Chin. Phys. Lett., 2013, 30(1): 070301
[8]	GU Ling-Ming. Coherent Control of Photon Transmission in a Coupled-Resonator Waveguide Embedded in a Semiconductor Quantum Dot[J]. Chin. Phys. Lett., 2012, 29(10): 070301
[9]	TIAN Wei, CHEN Bin, XU Wei-Dong. Controlling Single-Photon Transport along an Optical Waveguide by using a Three-Level Atom[J]. Chin. Phys. Lett., 2012, 29(3): 070301
[10]	Jamieson M. J., Ouerdane H., . Parameters for Cold Collisions of Lithium and Caesium Atoms**[J]. Chin. Phys. Lett., 2011, 28(6): 070301
[11]	WANG Yi, ZHANG Jing-Tao, REN Xiang-He, XU Zhi-Zhan, GUO Dong-Sheng. Photoelectron Angular Distributions of Positronium in Intense Laser Field[J]. Chin. Phys. Lett., 2009, 26(12): 070301
[12]	LIN Sheng-Lu, ZHOU Hui, XU Xue-You, JIA Zheng-Mao, DENG Shan-Hong. Semiclassical Calculations of Autoionization Rate for Lithium Atoms in Parallel Electric and Magnetic Fields[J]. Chin. Phys. Lett., 2008, 25(12): 070301
[13]	Itsuki Banno, Kazumi Fujima. Direct Evaluation of Transition Amplitude Using Determinant of Wave Operator in One-Dimensional Potential Scattering System[J]. Chin. Phys. Lett., 2007, 24(11): 070301
[14]	XU Tian, CAO Zhuang-Qi, OU Yong-Cheng, ZHU Guo-Long. Accurate Bound-State Spectra for Hydrogenic Donors in GaAs--(Ga, Al)As Quantum Dots[J]. Chin. Phys. Lett., 2005, 22(11): 070301
[15]	LIU Yi-Bao, PANG Wen-Ning, DING Hai-Bing, SHANG Ren-Cheng. Analysis of Observable Quantities from Excited Rubidium Impacted by Electrons at Low Incident Energy[J]. Chin. Phys. Lett., 2005, 22(6): 070301

Viewed

Full text

Abstract