With semi-classical approximation, thermodynamic properties of Fermi gas trapped in both gravity field and magnetic field are studied. By using theoretical analysis and numerical simulation, influence of gravity field on thermodynamic properties of the system in strong magnetic field is analyzed. It shows that, compared with the case of strong magnetic field only, gravity field makes the energy, chemical potential reduced. With rising temperature, influence of gravity field on chemical potential is gradually enlarged. There is a maximal influence of gravity field on heat capacity. Gravity field makes oscillation of heat capacity almost unchangeable while oscillation center of chemical potential shift down.

With quasi-classical approximations, statistic properties of Fermi gas in a strong magnetic field at high temperatures are studied. Analytical statistic characteristic quantities are given,and effects of magnetic field as well as temperature on statistic properties of the system are analyzed. Compared with a system in low temperatures.statiBtic characteristic quantities of Fermi gas in a strong magnetic field at high temperatures do not oscillate.The magnetic field deorease total energy of the system,and increases the chemical potential,heat capacity,entropy,pressure and stability of the system-The higher the temperature is,the weaker effects of magnetic field on total energy and heat caDacity and the stronger effects on chemical potential are.

We study distribution of particles in Bose-Einstein condensation and ground state energy of condensate by solving a G-P equation with Fourier-Grid-Hamiltonian(F-G-H) method. It is shown that particle density in condensate center increases and radius of condensate decreases as intensity of power-law potential or frequency of harmonic potential is increased or repulsive interaction between particles is decreased. The ground state energy of BEG increases with increasing of total particle number, repulsive interaction between particles, frequency of harmonic potential or intensity of power-law potential. Thomas-Fermi approximation results approximate to numerical results as particle number increases. It is shown that Thomas-Fermi approximation is a good method with large particle numbers. For less particle numbers, numerical method should be used.