Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

doi:10.1088/1674-1056/ac3653

中国物理B ›› 2022, Vol. 31 ›› Issue (5): 50311-050311.doi: 10.1088/1674-1056/ac3653

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

Yi-Cai Zhang(张义财)

School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China

收稿日期:2021-10-05 修回日期:2021-11-02 出版日期:2022-05-14 发布日期:2022-04-09
通讯作者: Yi-Cai Zhang,E-mail:zhangyicai123456@163.com E-mail:zhangyicai123456@163.com
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant No.11874127).

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

Yi-Cai Zhang(张义财)^†

School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China

Received:2021-10-05 Revised:2021-11-02 Online:2022-05-14 Published:2022-04-09
Contact: Yi-Cai Zhang,E-mail:zhangyicai123456@163.com E-mail:zhangyicai123456@163.com
About author:2021-11-4
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant No.11874127).

摘要/Abstract

摘要： We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential. It is found that, in the presence of a Coulomb potential of type I (with three equal diagonal elements), similarly to that in the two-dimensional case, the flat band could not survive. At the same time, the flat band states are transformed into localized states with a logarithmic singularity near the center position. In addition, the wave function near the origin would collapse for an arbitrarily weak Coulomb potential. Due to the wave function collapses, the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter. For a Coulomb potential of type II, there exist infinite bound states that are generated from the flat band. Furthermore, when the bound state energy is very near the flat band, the energy is inversely proportional to the natural number, e.g.,$E_n\propto$ 1/n, n=1,2,3,... It is expected that the 1/n energy spectrum could be observed experimentally in the near future.

关键词: wave function collapses, flat band, infinite bound states

Abstract: We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential. It is found that, in the presence of a Coulomb potential of type I (with three equal diagonal elements), similarly to that in the two-dimensional case, the flat band could not survive. At the same time, the flat band states are transformed into localized states with a logarithmic singularity near the center position. In addition, the wave function near the origin would collapse for an arbitrarily weak Coulomb potential. Due to the wave function collapses, the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter. For a Coulomb potential of type II, there exist infinite bound states that are generated from the flat band. Furthermore, when the bound state energy is very near the flat band, the energy is inversely proportional to the natural number, e.g.,$E_n\propto$ 1/n, n=1,2,3,... It is expected that the 1/n energy spectrum could be observed experimentally in the near future.

Key words: wave function collapses, flat band, infinite bound states

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Pm (Relativistic wave equations) 67.85.-d (Ultracold gases, trapped gases)

Yi-Cai Zhang(张义财). Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system[J]. 中国物理B, 2022, 31(5): 50311-050311.

Yi-Cai Zhang(张义财). Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system[J]. Chin. Phys. B, 2022, 31(5): 50311-050311.

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Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

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