Question

Explain the phenomena of "Bose-Einstein condensation" and find the critical temperature $T_{c}$ below which Bose-Einstein condensation takes place.

Show that Bose-Einstein condensation does not occur in tow dimensions.

п-1 1 gn(2) T(n) х" da 1er-1 Г(п)

Answer 1

Tha Qange accumulation Boson panti le Singla gound staie is called don sation Bose Ein stein Conden Soution Con E aken placo in Space momem tum Bose -Einstein Bunction Nous T-xa2 2 (2nmks N-No mo pon tice in excited s N-No = Ne Qange valus FO smallgn valun d Use d We ()7B Qunction2) Ne mond to ni 22 2 (42) Ne

N Ne , most ppantic le asa in the enccited states is de de7 mine d Bnom A3 Ban m Ne oll eccited słales aru pan tcbas hau Nem &0 that m N-Ne emd up in the Astaun d state an dansat on NN = A3 B.E 42 28m h3 213 h3 2m J2 2) N j doal take Bose as Confina d On in sogi A in 2D. OScea state panticls 'in exited No A 2TPd P 2 Ne A 2 Tm kg T (2)B h2 N Condom sation Suquiu t 1 nus A2 = ) Now P

Bollous Tu=0. dos not Condn Sati m So B.E on laos TC OCcun