论文标题
量子多体系统的自由下落
Free Fall of a Quantum Many-Body System
论文作者
论文摘要
自由秋季问题的量子版本通常是在本科量子力学课程中被跳过的主题，因为其讨论通常需要在通风函数上构建的Wavepackets（这是一个困难的计算）。相反，在这里，我们表明，通过利用量规变换，可以很好地简化问题，以及对一般的多体系统的简化，这与参考框架从实验室框架到与下落系统的一个相处的变更相对应。使用这种方法，外部重力电位中粒子的量子力学问题将减少到更简单的粒子，而Schrödinger方程中不再有任何重力电位。有启发性的是，可以将相同的过程用于具有外部重力潜力和两体颗粒间电位的多体系统，这是粒子之间距离的函数。该主题提供了一个量子多体系统的有用和教学示例，该系统可以用简单的术语进行分析描述。
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds to a change of reference frame from the laboratory frame to the one comoving with the falling system. Using this approach, the quantum mechanics problem of a particle in an external gravitational potential reduces to a much simpler one where there is no longer any gravitational potential in the Schrödinger equation. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential and a two-body interparticle potential that is a function of the distance between the particles. This topic provides a helpful and pedagogical example of a quantum many-body system whose dynamics can be analytically described in simple terms.
