A possible way from quantum mechanics to classical mechanics can be achieved with an exponential substitution used in the Schrödinger equation, and then considering the classical limit. This gives a picture of classical fluid and an ensemble of classical trajectories. In difference from this approach to the classical limit, while utilising the same substitution, we assume a minimum uncertainty wave packet. It is shown that this approach to the classical limit of quantum mechanics yields a single trajectory traced by the centroid of the minimum uncertainty wave packet. The momentum and the centroid of such packet satisfy the classical Hamilton-Jacobi equation.
Definitions of the momentum density, energy density, and densities of some other physical quantities are added to the standard Klein-Gordon theory. The densities introduced allow calculation of momentum and energy and their uncertainties of a localised Klein-Gordon field. It is shown that at certain conditions the momentum, energy, and potential energy of a localised Klein-Gordon field satisfy the relativistic Hamilton-Jacobi equation.
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