Quantum dynamics

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.

Keywords: 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.