Can Bose-Einstein condensate be written as non-linear wave equation (in terms of mean field approximation theory)? the equation is: enter image description here

source: http://xxx.tau.ac.il/abs/1308.2288

What I do understand by the Bose-Einstein condensate is, it is the state of atoms at very low temperatues and at the moment the atoms forget their previous identity. Therefore all the atoms stay in the same quantum state.

Am I right?

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    $\begingroup$ Why is this getting close votes? $\endgroup$ – Abhimanyu Pallavi Sudhir Nov 9 '13 at 5:01
  • $\begingroup$ Dont know why but I have not got canonical answer yet still. $\endgroup$ – user2378 Nov 9 '13 at 7:29

Bose-Einstein condensation is based on the indistinguishability and wave nature of particles, which are both basic concept of quantum mechanics. If you want to define Bose-Einstein condensation in one sentence, you can say it is the occupation of the lowest quantum state of the external potential by a large fraction of bosons forming the system. Particles are assumed to be bosons because only the Bose-Einstein statistics allows an arbitrary large number of particles to occupy one single quantum state.

The equation describing a condensate (or better the wave function of a condensate) is the Gross-Pitaevskii equation that is often referred as a non-linear Schroedinger equation.

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