基于新变分原理的阻尼粒子量子化
Quantization of Damping Particle Based On New Variational Principles
摘要：
本文提出了一种新的方法来求解运动方程不能化为哈密顿形式的力学系统。该方法基于一种新型的变分原理，它描述了一种关系：阻尼粒子与自由粒子共享一条公共的相曲线，在新的变分原理中，自由粒子的拉格朗日量可以看作是相空间中的拉格朗日密度。根据费曼理论，采用最小作用量原理对费曼路径积分公式进行修正，用拉格朗日密度代替拉格朗日量。在保守系统的情况下，修改减少到标准的费曼传播公式。作为一个例子，一个有摩擦的颗粒进行了详细的分析。
英文摘要：
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a relation: a damping particle may shares a common phase curve with a free particle, whose Lagrangian in the new variational principle can be considered as a Lagrangian density in phase space. According to Feynman's theory, the least action principle is adopted to modify the Feynman's path integral formula, where Lagrangian is replaced by Lagrangian density. In the case of conservative systems, the modification reduces to standard Feynman's propagator formula. As an example a particle with friction is analyzed in detail.
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