论文标题
关于量子力学中Ehrenfest定理不完整的考虑因素
Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics
论文作者
论文摘要
我们描述了一项由我们的兴趣驱动的研究，以研究量子力学中eHrenfest定理的不完整性，并解决有关哈密顿操作员是否足以简化巨型观察时间衍生物的表达合理的疑问，以促进通常在量子力学中发现的量子衍生物的表达。该研究通过考虑简单的量子系统“一维盒中的粒子”来发展。我们提出了理论论点，以支持他给出的表述中Ehrenfest定理的不完整性，同意一些作者已经发表的类似发现，并用静电场中电荷的数值示例证实了它们。这项研究的内容对学士和硕士学生应该很有用。我们希望，讨论的风格是为了激发学生独立思考的能力而量身定制的。
We describe a study motivated by our interest to examine the incompleteness of the Ehrenfest's theorem in quantum mechanics and to resolve a doubt regarding whether or not the hermiticity of the hamiltonian operator is sufficient to justify a simplification of the expression of the macroscopic-observable time derivative that promotes the one usually found in quantum-mechanics textbooks. The study develops by considering the simple quantum system "particle in one-dimensional box". We propose theoretical arguments to support the incompleteness of the Ehrenfest's theorem in the formulation he gave, in agreement with similar findings already published by a few authors, and corroborate them with the numerical example of an electric charge in an electrostatic field. The contents of this study should be useful to Bachelor and Master students; the style of the discussions is tailored to stimulate, we hope, the student's ability for independent thinking.
