• Mr. Ajay Kumar
• Dr. Sushil Kumar Jamariar
• Mr. Yashwant Singh
• Mr. Raju kumar Das

Abstract This project is based on the discussion of the mean field theory for the dilute base gas then there is derivation of the Gross- pitaeskii equation for the order parameter and we have used it to calculate the ground state energy of the system , then we discuss Bogoliubov model , it is a theory beyond mean field and takes in to account the flucturiton of order parameter . We introduce BogoLiubov effective Hamiltonion , discuss its diagonal – ization by means of bogoliubov transformation and calculate the correction of the ground state energy arising from the quantum flutuition then we discuss within the bogolivbov model the effects of weak external random potential we have also studied the behavior of the one body density matrix

Keywords : The non- interacting Bose gas, Condensed Phase , Normal Phase, The Gross pita evskil equation , The thomas Fermi approximation, Dilute Bose gas, Gross- pitaevskil equation, Ground state energy .

"A new prospect on Bose- Einstein Condensation", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.10, Issue 12, page no.f640-f643, December-2023, Available :http://www.jetir.org/papers/JETIR2312578.pdf

"A new prospect on Bose- Einstein Condensation", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.10, Issue 12, page no. ppf640-f643, December-2023, Available at : http://www.jetir.org/papers/JETIR2312578.pdf