经典运动方程在多大程度上决定了量子化方案?
To what extent do the Classical Equations of Motion Determine the Quantization Scheme?
摘要:
考虑一个粒子在(1+1)时空中运动的简单例子。我们以谐振子为例。我们确认的声明,经典的运动方程不确定在所有的量化方案。为此,我们使用两个不等价的拉格朗日函数,产生欧拉-拉格朗日方程,具有相同的一组解决方案。我们详细介绍了这两种情况下的计算,以强调它们之间发生的差异。
英文摘要:
A simple example of one particle moving in a (1+1) space-time is considered. As an example we take the harmonic oscillator. We confirm the statement that the classical Equations of Motion do not determine at all the quantization scheme. To this aim we use two inequivalent Lagrange functions, yielding Euler-Lagrange Equations, having the same set of solutions. We present in detail the calculations of both cases to emphasize the differences occuring between them.
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