ω tần số góc là một hằng số. a) Tính chức năng phân vùng kinh điển của ZC hệ thống, B đối với trường hợp các hạt là boson. b) Tính chức năng phân vùng kinh điển của hệ thống ZC, F đối với trường hợp các hạt được Fermion. 2. Hãy xem xét chiều một loại khí có chứa N-tương tác electron chuyển động theo hướng x. | 5. Exam Winter 2010 A Problems 1. Two identical non-interacting particles each having mass M are confined in a one dimensional parabolic potential given by V x 2Mw2 2 where the angular frequency w is a constant. a Calculate the canonical partition function of the system Zc B for the case where the particles are Bosons. b Calculate the canonical partition function of the system Zc F for the case where the particles are Fermions. 2. Consider a one dimensional gas containing N non-interacting electrons moving along the x direction. The electrons are confined to a section of length L. At zero temperature T 0 calculate the ratio U sF between the total energy of the system U and the Fermi energy f. 3. Consider an ideal classical gas at temperature T. The set of internal eigenstates of each particle in the gas when a magnetic field H is applied contains 2 states having energies _ 0H and 0H where the magnetic moment 0 is a constant. Calculate the magnetization of the system which is defined by M dH 2 T where F is the Helmholtz free energy. 4. Note replace this with Ex. in the lecture notes Consider an ideal gas made of N electrons in the extreme relativistic limit. The gas is contained in a box having a cube shape with a volume V L3. In the extreme relativistic limit the dispersion relation k is modified the energy of a single particle quantum state having a wavefunction given by x y z LF sin kxx sin kyy sin kzz Chapter 5. Exam Winter 2010 A is given by e k kc where c is the speed of light and where k yJkX ky k ị contrary to the non-relativistic case where it is given by e k 2k2 2M . The system is in thermal equilibrium at zero temperature T 0. Calculate the ratio p U between the pressure p and the total energy of the system U. 5. Consider a mixture of two classical ideal gases consisting of Na particles of type A and Nb particles of type B. The heat capacities cp A and cV A cp B and cV b at constant pressure and at constant volume respectively of gas A