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General solution of Schrödinger equation and electron transition in superlattice multi-quantum well

Luo Xiao-Hua

General solution of Schrödinger equation and electron transition in superlattice multi-quantum well

Luo Xiao-Hua
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  • Supposing that the quantum well of a superlattice is a periodic potential well of an arbitrary shape, the motion problem of electrons in the superlattice can be reduced into the motion in a periodic field. From the Schrödinger equation and its general solution, the dispersion equation of the system can be derived using Bloch theory and the transfer matrix method in the framework of quantum mechanics; and the electronic transitions of the multi-quantum well for the superlattice can be discussed in parabolic approximation. Results show that the radiation energy is located at the infrared, far infrared or terahertz band.
    [1]

    Gudiksen M S, Lauhon L J, Wang J F, Smith D C, Lieber C M 2002 Nature 415 617

    [2]

    Urban J J, Talapin D V, Shevchenko E V, Kagan C R Murray C B 2007 Nature Materials 6 115

    [3]

    Miura K, Iguchi Y, Tsubokura M, Kawamura Y 2013 Journal of Applied Physics 113 143506

    [4]

    Chen Y, Ouyang Z, Gu M, Cheng W L 2013 Advanced Materials 25 80

    [5]

    Yakushiji K, Saruya T, Kubota H, Fukushima A 2010 Applied Physics Letters 97 32508

    [6]

    Zhang M, Shao M Z, Luo S Y 2007 Chin. J. Luminescence 28 679 (in Chinese) [张梅, 邵明珠, 罗诗裕 2007 发光学报 28 679]

    [7]

    Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210

    [8]

    Liu H Z, Luo S Y, Shao M Z 2013 Chin. Phys. B 22 047807

    [9]

    Luo S Y, Li H T, Wu M Y, Wang S J, Ling D X, Zhang W F, Shao M Z 2010 Acta Phys. Sin. 59 15766 (in Chinese) [罗诗裕, 李洪涛, 吴木营, 王善进, 凌东雄, 张伟风, 邵明珠 2010 物理学报 59 15766]

    [10]

    Xu Z C, Chen J X, He L 2012 Laser & Infrared 42 45 (in Chinese) [徐志成, 陈建新, 何力 2012 激光与红外 42 45]

    [11]

    Feng X Y, Lu Y, Jiang L, Zhang G L, Zhang C W, Wang P J 2012 Acta Phys. Sin. 61 057101 (in Chinese) [冯现徉, 逯瑶, 蒋雷, 张国莲, 张昌文, 王培吉 2012 物理学报 61 057101]

    [12]

    Li P P, Tang H B, She W L, 2012 Acta Optica Sinica 32 0619004 (in Chinese) [李培培, 唐海波, 佘卫龙 2012 光学学报 32 0619004]

    [13]

    Sun W F, 2012 Acta Phys. Sin. 61 1171041 (in Chinese) [孙伟峰 2012 物理学报 61 1171041]

    [14]

    Xiao H J, Luo X H, Deng C L, Shao M Z 2011 Seim. Optoelectronics 31 422 (in Chinese) [肖慧娟, 罗晓华, 邓成良, 罗诗裕, 邵明珠 2011 半导体光电 31 422]

    [15]

    Luo D Y, Shao M Z, Luo X H 2010 Sci. Chin. (Physics, Mechanics & Astronomy) 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学(物理学, 力学和天文学) 40 207]

    [16]

    Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]

    [17]

    Haar D T 1960 Problems in Quantum Mechanics (London: Infosearch Limited) p246

  • [1]

    Gudiksen M S, Lauhon L J, Wang J F, Smith D C, Lieber C M 2002 Nature 415 617

    [2]

    Urban J J, Talapin D V, Shevchenko E V, Kagan C R Murray C B 2007 Nature Materials 6 115

    [3]

    Miura K, Iguchi Y, Tsubokura M, Kawamura Y 2013 Journal of Applied Physics 113 143506

    [4]

    Chen Y, Ouyang Z, Gu M, Cheng W L 2013 Advanced Materials 25 80

    [5]

    Yakushiji K, Saruya T, Kubota H, Fukushima A 2010 Applied Physics Letters 97 32508

    [6]

    Zhang M, Shao M Z, Luo S Y 2007 Chin. J. Luminescence 28 679 (in Chinese) [张梅, 邵明珠, 罗诗裕 2007 发光学报 28 679]

    [7]

    Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210

    [8]

    Liu H Z, Luo S Y, Shao M Z 2013 Chin. Phys. B 22 047807

    [9]

    Luo S Y, Li H T, Wu M Y, Wang S J, Ling D X, Zhang W F, Shao M Z 2010 Acta Phys. Sin. 59 15766 (in Chinese) [罗诗裕, 李洪涛, 吴木营, 王善进, 凌东雄, 张伟风, 邵明珠 2010 物理学报 59 15766]

    [10]

    Xu Z C, Chen J X, He L 2012 Laser & Infrared 42 45 (in Chinese) [徐志成, 陈建新, 何力 2012 激光与红外 42 45]

    [11]

    Feng X Y, Lu Y, Jiang L, Zhang G L, Zhang C W, Wang P J 2012 Acta Phys. Sin. 61 057101 (in Chinese) [冯现徉, 逯瑶, 蒋雷, 张国莲, 张昌文, 王培吉 2012 物理学报 61 057101]

    [12]

    Li P P, Tang H B, She W L, 2012 Acta Optica Sinica 32 0619004 (in Chinese) [李培培, 唐海波, 佘卫龙 2012 光学学报 32 0619004]

    [13]

    Sun W F, 2012 Acta Phys. Sin. 61 1171041 (in Chinese) [孙伟峰 2012 物理学报 61 1171041]

    [14]

    Xiao H J, Luo X H, Deng C L, Shao M Z 2011 Seim. Optoelectronics 31 422 (in Chinese) [肖慧娟, 罗晓华, 邓成良, 罗诗裕, 邵明珠 2011 半导体光电 31 422]

    [15]

    Luo D Y, Shao M Z, Luo X H 2010 Sci. Chin. (Physics, Mechanics & Astronomy) 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学(物理学, 力学和天文学) 40 207]

    [16]

    Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]

    [17]

    Haar D T 1960 Problems in Quantum Mechanics (London: Infosearch Limited) p246

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  • Received Date:  30 August 2013
  • Accepted Date:  06 October 2013
  • Published Online:  05 January 2014

General solution of Schrödinger equation and electron transition in superlattice multi-quantum well

  • 1. Library, Chongqing Jiaotong University, Chongqing 400074, China

Abstract: Supposing that the quantum well of a superlattice is a periodic potential well of an arbitrary shape, the motion problem of electrons in the superlattice can be reduced into the motion in a periodic field. From the Schrödinger equation and its general solution, the dispersion equation of the system can be derived using Bloch theory and the transfer matrix method in the framework of quantum mechanics; and the electronic transitions of the multi-quantum well for the superlattice can be discussed in parabolic approximation. Results show that the radiation energy is located at the infrared, far infrared or terahertz band.

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