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Free-fall in a uniform gravitational field in noncommutative quantum mechanics

机译:非交换量子力学中均匀引力场中的自由落体

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摘要

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]
机译:我们在非交换量子力学(NCQM)的背景下研究量子粒子的自由落体。假设二维构造空间的坐标之间的正则类型是非交换性的,我们考虑了被困在引力井中的中性粒子,并精确地解决了能量本征值问题。通过利用来自GRANIT实验的实验数据,其中确定了自由下落的量子超冷中子的第一能级,我们在非交换性参数上施加了上限。我们还研究了在NCQM中均匀重力场中移动的量子粒子的飞行时间。这与弱等价原理有关。当我们考虑静止的能量本征状态,即离域状态时,必须通过适当耦合到粒子的量子时钟来测量飞行时间。通过将时钟视为很小的扰动,我们解决了相关的(固定)散射问题,并证明了在远离转折点进行测量时,飞行时间等于经典结果。该结果被解释为对等原则在NCQM领域的扩展。 (C)2010美国物理研究所。 [doi:10.1063 / 1.3466812]

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