Propagation of General Wave Packets in Some Classical and Quantum Systems

在量力学，一个波浪包的中心精确被定义为概率的中心。center-of-probability 速度描述波浪包的全部运动。在古典物理，到量力学的 center-of-probability 速度没有精确对应物，尽管有事实在那里在文学存在为电磁波的至少八不同速度。我们建议 center-of-energy 速度在古典物理系统描述一般波浪包的全部运动。它是可测量的数量，并且是为连续、分离的系统的井 denned。为电磁波包，它是精力运输的速度的归纳。在几个古典系统的一般波浪包被学习， center-of-energy 速度以分散关系和 Fourier 系数计算、表示。这些系统在一种尺寸在一种尺寸，和古典海森堡模型包括绳题目到外部力量，单原子的链和两价的链。在大多数情况中， center-of-energy 速度把 forquasi 单色的波浪包归结为组速度。因此，它也看起来是组速度的归纳。相对论的迪拉克方程的波浪包简短被讨论。

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group Velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.