Moving Picture and Hamilton-Jacobi Theory in Quantum Mechanics

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J-GLOBAL : 200901014932178108

J-GLOBAL : 200901024071764383

We propose a new picture, which we call the moving picture, in quantum mechanics. This picture provides the coordinate system which sticks to the particles. The Schrödinger equation in this picture is derived and its solution is examined. We also investigate the close relationship between the moving picture and the Hamilton-Jacobi theory in classical mechanics. This shows a new correspondence between classical and quantum mechanics. We examine the cases of the free particle and the harmonic oscillator, as an example of the usefulness of this picture.

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