Conditions under which a quantum particle can be described using classical quantities are studied. We investigate the wavefunction of a quantum particle submitted to a potential field for which all quantum effects vanish, even if Planck's constant is non-negligible. This problem is equivalent to the problem of the motion of a particle in a refringent medium. The indices of refraction of such media are found. In these media, quantum particles have classical momenta, while their wave properties are described by the wave-optics equation with a characteristic length equal to the de Broglie wavelength $ƛ$. In the 1D case, the particle cannot be found in the region near the origin, since the index of refraction tends to infinity there. For the 3D case with central symmetry, the wave properties are determined by a function that has a resonance of width about $2ƛ$. Experimental verification of theoretical predictions is discussed.

中文翻译：

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量子粒子在折射介质中的经典行为

研究了可以使用经典量描述量子粒子的条件。我们研究了一个量子粒子的波函数，它被置于一个所有量子效应都消失的势场中，即使普朗克常数是不可忽略的。这个问题等价于粒子在折射介质中的运动问题。发现了这种介质的折射率。在这些介质中，量子粒子具有经典动量，而它们的波动特性由波光方程描述，其特征长度等于德布罗意波长$蛟$. 在 1D 情况下，在原点附近的区域中找不到粒子，因为那里的折射率趋于无穷大。对于具有中心对称性的 3D 情况，波特性由具有约$2蛟$. 讨论了理论预测的实验验证。