Abstract
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.
Keywords: Wave function, Wave packet, Group velocity, Canonical momentum, Proper time, Lagrangian, Amplitude function, Distribution function, Normalization, Mass density, Metric tensor, Quantization rule.
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