arXiv quant-ph/06061722006-06-20quant-ph

量子力学与弱等效原理

Quantum Mechanics and the Weak Equivalence Principle

Stella Huerfano, Sarira Sahu, M. Socolovsky

备注：: 8 pages, 2 eps figures

摘要：

我们将费曼路径积分方法用于非相对论性量子力学的两个方面。首先，我们推导出一个无自旋粒子在均匀但不一定是恒定加速的参考系中运动的拉格朗日量;然后，应用强等效原理（SEP），我们得到了一个粒子在惯性系中的薛定谔方程，并存在一个均匀和恒定的重力场。其次，利用Feynman传播子，我们传播了一个初始高斯波包，最终的波函数和概率密度依赖于m/hbar的比值，其中m是粒子的惯性质量，从而展示了量子力学违反弱等效原理的事实。虽然由于快速振荡的波函数不存在于经典极限，概率密度是明确的，质量无关时，hbar去0，显示的WEP恢复。最后，在量子水平上，较重的粒子不一定比较轻的粒子下落得快;这取决于粒子的初始和最终公共位置和时间之间的关系。

英文摘要：

We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying the strong equivalence principle (SEP) we obtain the Schroedinger equation for a particle in an inertial frame and in the presence of a uniform and constant gravity field. Second, using the associated Feynman propagator, we propagate an initial gaussian wave packet, with the final wave function and probability density depending on the ratio m/hbar, where m is the inertial mass of the particle, thus exhibiting the fact that the weak equivalence principle (WEP) is violated by quantum mechanics. Although due to rapid oscillations the wave function does not exist in the classical limit, the probability density is well defined and mass independent when hbar goes to 0, showing the recovery of the WEP. Finally, at the quantum level, a heavier particle does not necessarily falls faster than a lighter one; this depends on the relations between the initial and final common positions and times of the particles.

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