Quaternion Effective Mass and Particle Velocity
Quaternion Effective Mass and Particle Velocity
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四元数有效质量和粒子速度
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
V. Ariel
中科院分区：
文献类型：
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作者：
V. Ariel
在这项工作中，我们建议应用超复数-四元数-的相对论性粒子和粒子在非抛物半导体的有效质量的定义。我们证明，四元数定义的有效质量产生的相对论能量动量色散关系和相对论粒子质量的绝对值。然后，由于电磁相互作用的存在，我们引入了一个四元数电磁质量。最后，我们定义了四元数质点速度。我们将此定义应用于非抛物各向同性半导体材料，如InSb，并证明在高电场下的电子速度饱和。我们比较本模型实验测得的电子速度在高电场在InSb。这里呈现的结果似乎展示了狭义相对论的数学和物理概念的另一种方法。
In this work, we propose applying hyper-complex numbers - quaternions - to the definition of the effective mass of relativistic particles and particles in non-parabolic semiconductors. We demonstrate that the quaternion definition of the effective mass generates the relativistic energy-momentum dispersion relation and absolute value of the relativistic particle mass. Then, we introduce a quaternion electromagnetic mass due to presence of electromagnetic interaction. Finally, we define the quaternion particle velocity. We apply this definition to non-parabolic isotropic semiconductor materials, such as InSb, and demonstrate electron velocity saturation at high electric fields. We compare the present model to experimentally measured electron velocity at high electric field in InSb. The results presented here seem to demonstrate an alternative approach to mathematical and physical concepts of special relativity.