To what extent do the Classical Equations of Motion Determine the Quantization Scheme?

Details To what extent do the Classical Equations of Motion Determine the Quantization Scheme? To what extent do the Classical Equations of Motion Determine the Quantization Scheme?

2000-12-04

arxiv.org/abs/math-ph/0012005v1

Physics

Mathematical Physics

LaTeX 20 pages

Scientific paper

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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