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In this chapter, we derived some elements of quantum mechanics, which are essential
for the further development of our theory: the momentum of a system of Fermions in the
second quantization, the coordinate and momentum of a harmonic oscillator as a unique
operator at two different moments of time, Boson and Fermion operator algebra, coherent
states, the electron-field interaction, the quantization of the electromagnetic field, Boson
and Fermion distributions, and densities of states in a degenerate, or a non-degenerate
system of Fermions. Our starting point is the wave nature of a quantum particle, the
Hamiltonian equations were obtained as group velocities in the two conjugate spaces of the
wave, of the coordinates and of the momentum. In this way, the Schr¨odinger equation and
the electron-field potential of interaction are obtained from quantum equations generated
by the particle wave function.
Wave-function, group velocity, state vector, Schr¨odinger equation, eigenstate,
eigenvector, density matrix, operator, Hermitian conjugate, representation, Maxwell
equations, Fermion, Boson, Fermi-Dirac distribution, Bose-Einstein distribution, Fourier
transform, Hamiltonian, Lagrangian, Hamilton equations, Lagrange equation.
Center of Advanced Studies in Physics of the Romanian Academy, Bucharest Romania.