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Thede Broglie-Bohm causal interpretation of quantum mechanics and its application to some simple systems.

机译:量子力学的De Broglie-Bohm因果解释及其在某些简单系统中的应用。

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摘要

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrodinger, Pauli and Dirac hydrogen eigenstates. In the Schrodinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrodinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the z-axis. Electron trajectories are also found for the 1s--2p0 transition problem under the Schrodinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard |psi|2 distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the |psi|2 distribution. Several promising avenues for future research are discussed.
机译:讨论了量子力学的de Broglie-Bohm因果因果解释,并将其应用于几种情况下的氢原子。记录了对因果程序的突出批评并给出了答复;有人认为,德布罗意-博姆理论对物理学意义重大。使用因果理论,可以找到常规薛定inger,保利和狄拉克氢本征态的电子轨迹。在薛定inger的情况下,使用附加术语来解释自旋。该术语在理论的原始表述中不存在,但对于将理论嵌入相对论的表述是必不可少的。在Schrodinger,Pauli和Dirac的情况下,本征态轨迹显示为圆形,电子运动围绕z轴旋转。在薛定inger方程下,还发现了1s--2p0跃迁问题的电子轨迹。结果表明,该转变可以通过将轨迹与相关本征态轨迹进行比较来表征。计算出的轨迹的结构与量子分布朝标准psi | 2分布(量子平衡)可能演化的问题有关。这个过程称为量子弛豫。一般将过渡问题包括半经典辐射激发的氢中所有可能的过渡,并根据它们对分布向| psi | 2分布演变的影响,对所发现的所有轨迹进行了检查。讨论了未来研究的一些有希望的途径。

著录项

  • 作者

    Colijn, Caroline.;

  • 作者单位

    University of Waterloo (Canada).;

  • 授予单位 University of Waterloo (Canada).;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2004
  • 页码 205 p.
  • 总页数 205
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

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