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This doctoral thesis is primarily comprised on the analytical and numerical analysis of the electrostatic dynamic potential associated with a moving test particle in the three disciplines of quantum plasmas namely semi-conductors, astrophysical dusty and relativistic quantum plasmas in the presence of homogenous magnetic field. The study of four aspects of electrostatic potential in quantum plasmas is presented based on the published work. A qualitative analysis of dispersive properties in homogeneous magnetized plasmas is done with fluid approach known as Quantum Hydrodynamic model. Above all, wake potential is studied in the semi-conductor quantum plasmas where an external source of electron beam is taken for exciting the plasma wave. Next, the dense quantum dusty plasma system is taken for the study of wake potential taking into account the quantum effects exhibited by the Fermi pressure, tunneling and exchange-correlation potential of the Fermi particles. Afterwards, the relativistic quantum plasma system is taken for the study of interesting characteristics of wake potential where tunneling potential is ignored in the comparison of Fermi pressure. The behavior of the linear potential is observed similar in the non relativistic plasma either for semiconductor or dusty plasma with a natural difference of higher density. While in relativistic quantum plasma, a subsonic potential is noticed contrary to the supersonic potential existing in non-relativistic plasmas. At the end, linear and KdV type nonlinear cases are studied at very high magnetic field taking into account the Landau quantization of magnetic field. The structural characteristics of the potential pulse and of the associated electric field strongly depend on the magnetic field, in addition to the quantum parameter H= ħ??? 2????? .
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