中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10302-010302.doi: 10.1088/1674-1056/ae111e

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Electric-type Stern-Gerlach effect

Jiang-Lin Zhou(周蒋麟)1, Zou-Chen Fu(傅邹晨)1, Choo Hiap Oh(胡祖协)2,, and Jing-Ling Chen(陈景灵)3,†   

  1. 1 School of Physics, Nankai University, Tianjin 300071, China;
    2 Centre for Quantum Technologies and Department of Physics, National University of Singapore 117543, Singapore;
    3 Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
  • 收稿日期:2025-09-02 修回日期:2025-09-29 接受日期:2025-10-09 发布日期:2025-12-30
  • 通讯作者: Jing-Ling Chen E-mail:chenjl@nankai.edu.cn
  • 基金资助:
    This project is supported by the Quantum Science and Technology-National Science and Technology Major Project of China (Grant No. 2024ZD0301000) and the National Natural Science Foundation of China (Grant No. 12275136).

Electric-type Stern-Gerlach effect

Jiang-Lin Zhou(周蒋麟)1, Zou-Chen Fu(傅邹晨)1, Choo Hiap Oh(胡祖协)2,, and Jing-Ling Chen(陈景灵)3,†   

  1. 1 School of Physics, Nankai University, Tianjin 300071, China;
    2 Centre for Quantum Technologies and Department of Physics, National University of Singapore 117543, Singapore;
    3 Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
  • Received:2025-09-02 Revised:2025-09-29 Accepted:2025-10-09 Published:2025-12-30
  • Contact: Jing-Ling Chen E-mail:chenjl@nankai.edu.cn
  • Supported by:
    This project is supported by the Quantum Science and Technology-National Science and Technology Major Project of China (Grant No. 2024ZD0301000) and the National Natural Science Foundation of China (Grant No. 12275136).

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摘要： The Stern-Gerlach (SG) experiment is a fundamental experiment for revealing the existence of “spin”. In this experiment, beams of silver atoms are sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac’s equation with a potential barrier, revealing an extraordinary spin effect. Beams of Dirac particles can be regarded as matter waves. Based on Dirac’s equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can exhibit notable spatial shifts, which depend on the spin direction and the incident angle of the wave. The electric-type SG effect has potential applications for separating Dirac particles with different spin directions and for estimating the spin direction of Dirac particles. Some discussions related to the interaction between spin and the electric field are also presented.

关键词: Dirac’s electron, reflection and transmission, spin, Stern-Gerlach experiment, electric-type Stern-Gerlach effect

Abstract: The Stern-Gerlach (SG) experiment is a fundamental experiment for revealing the existence of “spin”. In this experiment, beams of silver atoms are sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac’s equation with a potential barrier, revealing an extraordinary spin effect. Beams of Dirac particles can be regarded as matter waves. Based on Dirac’s equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can exhibit notable spatial shifts, which depend on the spin direction and the incident angle of the wave. The electric-type SG effect has potential applications for separating Dirac particles with different spin directions and for estimating the spin direction of Dirac particles. Some discussions related to the interaction between spin and the electric field are also presented.

Key words: Dirac’s electron, reflection and transmission, spin, Stern-Gerlach experiment, electric-type Stern-Gerlach effect

中图分类号:  (Relativistic wave equations)

  • 03.65.Pm
03.65.Nk (Scattering theory)