地球引力中中子的量子化
Quantization of neutron in Earth's gravity
摘要：
引力是宇宙中已知的四种力中最弱的一种。由于这样一个弱场，基本粒子的量子态肯定是非常浅的，因此将是一个实验上的挑战。最近，V. V. Nesvizhevsky等人进行了一项实验尝试，Nature 415，297（2002），以测量中子的量子态，其显示基态和少数激发态为\sim 10^{-12}eV。我们证明了限制在地球表面以上的中子的基态能量应为\sim 10^{-37}eV。实验观察到的能级比实际的能级深10^{25}倍，因此肯定不是由于地球的引力效应。因此，对参考文献\cite{nes1}的艰苦实验结果的正确解释是由于长度为L \sim 50μm的一维盒子的限制势，该限制势是由\cite{hansoon}之前评论的实验装置产生的。我们的结果对今后解决地球引力场中中子的浅能级问题提出了新的挑战。
英文摘要：
Gravity is the weakest of all four known forces in the universe. Quantum states of an elementary particle due to such a weak field is certainly very shallow and would therefore be an experimental challenge to detect. Recently an experimental attempt was made by V. V. Nesvizhevsky et al., Nature 415, 297 (2002), to measure the quantum states of a neutron, which shows that ground state and few excited states are \sim 10^{-12}eV. We show that the energy of the ground state of a neutron confined above Earth's surface should be \sim 10^{-37}eV. The experimentally observed energy levels are 10^{25} times deeper than the actual energy levels it should be and thus certainly not due to gravitational effect of Earth. Therefore the correct interpretation for the painstaking experimental results of Ref. \cite{nes1} is due to the confinement potential of a one dimensional box of length L \sim 50μm, generated from the experimental setup as commented before \cite{hansoon}. Our results thus creates a new challenge to the experimentalist to resolve the shallow energy levels of the neutron in Earth's gravitational field in future.
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