7.4 Bose Condensation Bose gas is particle systems have characteristics: • Homogeneous particle systems: the system has photon particles, the medon, atoms have even electrons these particles are Bose particles • Spin whole or zero • Interdependence between particles can be ignored 7.4 Bose Condensation •7.4.1   Apply Bose-Einstein distribution to calculate the total number of particles - Consider an energy interval : Suppose that in the interval d� has dN the energy level The number of particles in the range of d is: d dn(�) = dN (7.1) ( : the mean number of particles on an energy level) 7.4 Bose Condensation -•  Bose-Einstein distribution: (non-degenerate) According to theoretical mechanics: the number of standing wave has a modulus of wave vector within + d: dN( (7.2) 7.4 Bose Condensation We have : On the orther hand : => So put in (7.2):  (7.3) 7.4 Bose Condensation In quantum statistics, the particle state depends on have g=2s+1 spin orientation There are g possible states where the degenerate level of ℇ is g = 2s + (7.4) 7.4 Bose Condensation - Particles with energy in the range  dn( (7.5) The total number of particles of the system is N,so N= (7.6)  From this equation can identify some characteristics of Bose gas 7.4 Bose Condensation 7.4.2 Chemical potential properties a) Chemical potential 0 (7.5) then (-1) >0 => >1 with all values b) � decreases when T is increased Put U( (7.7) 7.4 Bose Condensation • We   have: = ==•We have then >0 then •Then � decreases when T is increased 7.4 Bose Condensation 7.4.3 Bose condensation phenomenon  Since μ is inversely proportional to T, when T decreases, μ increases (μ 0 then •Then � decreases when T is increased 7 .4 Bose Condensation 7 .4. 3 Bose condensation phenomenon  Since... (7.3) 7 .4 Bose Condensation In quantum statistics, the particle state depends on have g=2s+1 spin orientation There are g possible states where the degenerate level of ℇ is g = 2s + (7 .4) 7 .4 Bose. .. 7 .4 Bose Condensation -• Bose- Einstein distribution: (non-degenerate) According to theoretical mechanics: the number of standing wave has a modulus of wave vector within + d: dN( (7.2) 7 .4 Bose