论文标题
确定性量子力学：数学方程式
Deterministic Quantum Mechanics: the Mathematical Equations
论文作者
论文摘要
如果不浪费时间和精力，我们写下了量子系统的哈密顿量的条件，以使其数学上等同于确定性系统。这些是要考虑的方程式。特别注意“地方”的概念。制定了各种示例，然后进行系统的程序，以生成完全等效的经典进化法和量子哈密顿量。这里的新事物是，我们考虑互动，使它们尽可能笼统地保持一般性。如果我们将自己限制在足够低的能量状态下，则发现的量子系统会形成密集的集合。该类是离散的，仅仅是因为包含有限数量的经典状态的确定性模型集是离散的。与早期的怀疑相反，重力不需要。这足以使经典系统在时间尺度上起作用比所考虑的最大散射能的倒数要小得多。
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the equations to be considered. Special attention is given to the notion of 'locality'. Various examples are worked out, followed by a systematic procedure to generate classical evolution laws and quantum Hamiltonians that are exactly equivalent. What is new here is that we consider interactions, keeping them as general as we can. The quantum systems found, form a dense set if we limit ourselves to sufficiently low energy states. The class is discrete, just because the set of deterministic models containing a finite number of classical states, is discrete. In contrast with earlier suspicions, the gravitational force turns out not to be needed for this; it suffices that the classical system act at a time scale much smaller than the inverse of the maximum scattering energies considered.
