Question

Consider an 3-dimensional ideal bose gas system whose dispersion relation is given by
a) Find the mean occupation number of quantum state with a wave vector
b) Find the total number of particles $N_{1}$ at excited states and internal energy at temperature and express it in terms of Bose-Einstein integral and thermal wave length

h2k2 E hw 2m U (T gn(z; h2 1/2 2TmkBT T(

Answer 1

C) Nouw Use gramd Cano ni cal em semble -Ham panthtion umction exp(-pnn En +p.4) E n0,1,2,.. no,2,. - oCupahon Fim mumbe Now meam ms exp mr exp ms e (7-19) -1 2m

damo le anti tianunction Now SLom mo Noco mics PV E encp Now Base -Eis tein unctign (2 m ka T Y2 stade Noa dem sit 3/2 Y2

Calculate Nou we Cam - n-) (2m ) de 블 수 Now Panticle in oround stole No mum loes With E = o Put pE=x Now n ee 2 tam (2mkr}%/2 2 T N-No h3 (2) kQ 2() Now Ne = N-No Ne numbn & panticla (E0 in excled with Noco inten nal emargy 1 = Kg Tu