一个模拟非相对论量子力学系统的局域离散模型
A Local and Discrete Model Simulating Nonrelativistic Quantum Mechanical Systems
摘要：
本文提出了一个简单的模型，模仿量子力学（QM）的结果，而不使用复杂的波函数或非局域性。所提出的模型只使用整数值的数量和算术运算，特别是假设一个离散的时空下的一个欧几里德格的形式。所提出的方法将单个粒子的轨迹描述为随机行走。跃迁概率是几个量的简单函数，这些量要么在粒子准备过程中随机地与粒子相关联，要么存储在它们在行走过程中访问的晶格节点中。非相对论性QM预测被检索为类似制备的粒子系综的概率分布。考虑评估模型的方案包括自由粒子，恒定外力，谐振子，粒子在一个盒子里，和三角洲的潜力。
英文摘要：
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a discrete spacetime under the form of a Euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. Non-relativistic QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, and the Delta potential.
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