Bose-Einstein Condensation Theory for Any Integer Spin: Approach Based in Noncommutative Quantum Mechanics

A Bose-Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter and, at second order in , our procedure yields to the standard dipole-dipole interaction with 2 playing the role of the strength interaction parameter. The generalized Gross-Pitaevskii equation containing nonlocal dipolar contributions is found. For 52Cr isotopes = Cdd/4 becomes 10-11cm and, thus for this value of one cannot distinguish interactions coming from non-commutativity or those of dynamical origin. © 2022 World Scientific Publishing Company.