中国物理B ›› 2008, Vol. 17 ›› Issue (12): 4378-4381.doi: 10.1088/1674-1056/17/12/008

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Quantization rules for low dimensional quantum dots

曹庄琪1, 许田2, 方靖淮2   

  1. (1)Institute of Optics and Photonics, Shanghai Jiao Tong University, Shanghai 200240, China; (2)Physics department, Nantong University, Nantong 226001, China
  • 收稿日期:2008-03-26 修回日期:2008-04-14 出版日期:2008-12-20 发布日期:2008-12-20

Quantization rules for low dimensional quantum dots

Xu Tian (许田)a,  Cao Zhuang-Qi (曹庄琪)b, Fang Jing-Huai (方靖淮)a   

  1. a Physics department, Nantong University, Nantong 226001, China; b Institute of Optics and Photonics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2008-03-26 Revised:2008-04-14 Online:2008-12-20 Published:2008-12-20

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摘要： This paper applies the analytical transfer matrix method (ATMM) to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB (Wentzel, Kramers and Brillouin) method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK (Einstein, Brillouin and Keller) results or the wave function outcomes. From the comparisons, it finds that the semiclassical method (WKB, EBK or wave function) is inexact in such systems.

关键词: analytical transfer matrix method, quantization rules, energy eigenvalues, confining potential

Abstract: This paper applies the analytical transfer matrix method (ATMM) to calculate energy eigenvalues of a particle in low dimensional sharp confining potential for the first time, and deduces the quantization rules of this system. It presents three cases in which the applied method works very well. In the first quantum dot, the energy eigenvalues and eigenfunction are obtained, and compared with those acquired from the exact numerical analysis and the WKB (Wentzel, Kramers and Brillouin) method; in the second or the third case, we get the energy eigenvalues by the ATMM, and compare them with the EBK (Einstein, Brillouin and Keller) results or the wave function outcomes. From the comparisons, it finds that the semiclassical method (WKB, EBK or wave function) is inexact in such systems.

Key words: analytical transfer matrix method, quantization rules, energy eigenvalues, confining potential

中图分类号:  (Quantum dots)

  • 73.21.La
03.65.Ge (Solutions of wave equations: bound states) 03.65.Sq (Semiclassical theories and applications)