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I was hoping someone might be able to give a approachable explination of the Gross-Pitaevskii equation. All the sources I've been able to find seem to concentrate on the derivation, and I don't have the physics background to follow. From what I understand, however, is that the GP equation models the ground state of a collection of bosons (all in the same, lowest energy state) by using "some mean field theory approach". My main questions are

1) What are some of the assumptions that lead to the GP equation?

2) I've read that the GP is 'a nonlinear Schrodinger equation'. I recognize the form of the Schrodinger equation in the GP, but is the extra magnitude-of-psi-squared term part of the potential or something completely different? Intuitively, where does it come from and what does it mean?

3) What are some interesting and/or physically relevant potentials for the GP equation? I guess this is a vague question, but what kinds of potentials are Bose Einstein condensates frequently subjected to? For instance, in quantum mechanics we study the particle in a box and harmonic oscillator models - are these interesting/relevant in BE condensates as well?

Thanks!

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# Gross-Pitaevskii equation in Bose Einstein condensates

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