物理课件27-1.pptVIP

Chapter 27 Fermi and Bose Statistics Chapter 13 ~ classical statistics or kinetic theory, Microscopic particles are essentially quantal Classical or quantal? define a thermal (de Broglie) wavelength the fundamental laws of motion ~ Newton’s laws. granular property dominants — classical! a l or T T0 wave property is more important — quantal Degenerate temperature Spacing a Microscopic particles are essentially identical Anti-symmetric — fermion symmetric — boson 27.1 Fermions and Bosons Although the symmetry requirement for Fermions and Bosons are ultimately founded on experiment, it may be proven within the context of quantum field theory that *given general assumptions of locality, causality and Lorentz invariance: particles with odd half integer spin: Fermions particles with integer spin: Bosons Fermions: electrons, protons, neutrons, muons, neutrinos, and quarks etc. Composite particles: Fermions: 2H(deuterium), nuclei of 3H (triton), and 3He atoms etc. Bosons: photons, pions, mesons, and gluons etc. Bosons: 1H, nuclei of 2H (deuteron), nuclei of 4He, 4He atoms etc. 7Li, Na, 87Rb atoms. Second effect of identity One can count how many particles in certain energy level but can not specify. For size of macroscopic scale, energy levels are quasi-continuous. Independent particles in 3D box For one-dimensional case Quantum number n = ? to be fixed in next section Eq.(21.5.6) DOS: quasi-continuity: summation over quantum states ? integral g = 2s + 1 degeneracy due to spin quantum states For non-relativistic system, energy spectrum is We can write DOS as 27.2 Fermi-Dirac distribution For quantal ideal Fermi gases, Particles obey of Fermi-Dirac distribution b ? 1/kBT chemical potential Fermi energy T ? 0 (or b ? ? ) m ? EF = q : step function Fermi wavevector and Fermi temperature In k-space, particles only fill a zone k ? kF called Fermi sphere or Fermi sea. Fermi wave number For metal copper All excitation, exchange mainly involve particles nea