量子世界的新离散观
A new discrete view to the quantum world
摘要：
本文提出了一个新的相对论单电子系统的量子力学离散模型，其中粒子的运动由一个带有4-旋量的有向时空图描述，但没有任何连续的波函数。这些图只包含少量的类空间边，例如原子的基态由两个节点和一条边描述，并且相互作用只发生在节点处。其基础是相对论不变的“拉格朗日和”的极值原理，由此导出“场方程”和“运动方程”，从而完全确定了系统的状态（包括图中的节点）。作为模型的重要验证，绘制了原子定态Dirac方程的相应图形，并计算了正确的光谱（Sommerdan能级）。导出了离散薛定谔近似和相应的哈密顿和，给出了经典运动粒子在洛伦兹力作用下的正确方程。我希望，这种新的方法将有助于克服当前量子力学的一些问题，使波函数多余。
英文摘要：
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These graphs only consist of few space-like edges, e.g. the ground state of atoms is described by two nodes and one edge, and interactions only take place at the nodes. The fundament is an extremal principle for a relativistic invariant "Lagrangian sum", from which "field-equations" and "equations of motion" are derived, so the states (including the graph nodes) are completely determined. As important validations of the model, the corresponding graphs for the stationary Dirac-equation for the atom are drawn and the correct spectra are computed (Sommerfeld-levels). Also a discrete Schroedinger approximation and an associated "Hamiltonian sum" are derived and the correct equation of a classical moving particle under Lorentz-force is presented. I hope, that this new approach will help, to overcome some problems of current quantum mechanics by making the wave function superfluous.
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