标题： 最小长度、最大动量与量子力学的希尔伯特空间表示 显示英文标题

标题： Minimal length, maximal momentum and Hilbert space representation of quantum mechanics

摘要： Kempf 等人在文献[1]中制定了量子力学的希尔伯特空间表示，其中包含最小可测长度。最近，在双特殊相对论的背景下揭示了检验粒子的动量不能任意不精确，因此存在动量涨落的上限。考虑到这一成果，我们将Kempf的开创性工作{\it 等}推广到检验粒子也存在最大动量的情况。检验粒子动量存在上限提供了若干新颖且有趣的特点，其中一些在本文中进行了研究。 显示英文摘要

摘要： Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum cannot be arbitrarily imprecise and therefore there is an upper bound for momentum fluctuations. Taking this achievement into account, we generalize the seminal work of Kempf {\it et al.} to the case that there is also a maximal particles' momentum. Existence of an upper bound for the test particles' momentum provides several novel and interesting features, some of which are studied in this paper.