论文标题
关于量子粒子经典性的条件
On the conditions for the classicality of a quantum particle
论文作者
论文摘要
研究了使用经典量描述量子粒子的条件。考虑一维（1D）和三维（3D）问题。结果表明，当量子粒子与某些特定介质相互作用时，所有量子校正（从WKB意义上）的贡献之和严格消失。发现了这种介质的折射指标。在这种情况下，不假定普朗克常数的小。确定了这些介质中量子颗粒的动量和固定态的波函数。已经发现，对于1D情况，波函数与具有零结合能的测试粒子相似，在奇异的有吸引力的电位中，它承认“跌落”到中心。对于带有中央对称性的3D情况，描述具有经典动量的量子粒子的固定状态是由波函数定义的，波函数的宽度大约是两个de Broglie波长。
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum corrections (in the WKB sense) strictly vanishes, when a quantum particle interacts with some specific medium. The indices of refraction of such media are found. In this case, the smallness of the Planck constant is not assumed. The momenta of quantum particles in these media and the wave functions of stationary states are determined. It is found that, for the 1D case, the wave function is similar to that of the test particle with zero binding energy in a singular attractive potential, which admits "fall" to the center. For the 3D case with central symmetry, a stationary state, describing a quantum particle with a classical momentum, is defined by the wave function, which has the resonance of width about two de Broglie wavelengths.
