Proposal for the Quantum Mechanical Orbit Equation

概要

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The orbit equation for the motion of a quantum in a potential is proposed by defining uniquely the quantum mechanical momentum from the Schroedinger wave equation of a oneparticle system and using the Hamilton-Jacobi formalism. On this occasion it is necessary to introduce a new dynamical postulate, "initial condition", which is independent of the quantization condition as well as of the Schroedinger wave equation. The momentum is determined in such a way that it is approximately equal to the corresponding classical mechanical momentum in the classical region of validity of the coordinates. The momentum in the nonclassical region is in general very small in comparison with that in the classical region. The quantum-mechanical motion well corresponds to the classical motion. If a system is macroscopic, the motion of the particle is described by Newtonian mechanics and the quantization condition is of no validity. The "quantization of magnetic flux" derives from the quantization condition. It is closely related to the energy level structure of the atomic system. The above argument is applied to the scalar electromagnetic and sound wave equations to give the dynamical motion of a photon and a phonon without recourse to the so-called second quantization method.
理論物理学刊行会の論文
1965-09-25