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Quantum Particle as a Distribution of Matter

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In this chapter, we consider the wave function of a particle as a wavepacket describing the density amplitude in the coordinate space, and its inverse Fourier transform, as a wave function in the momentum space. We obtain the momentum from the mass Lagrangian in the time-dependent phase of the wave function, and the particle dynamics from the group velocities of these wave-packets in the two conjugate spaces of the coordinates and of the momentum. From the equality of the mass in the relativistic Lagrangian, which describes the matter dynamics, with the total mass as an integral of the density, we obtain the matter quantization.

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