I am a graduate student just started learning dispersive PDE in MSRI's summer program. I roughly finished reading the paper by Klainerman and Machedon "ON THE UNIQUENESS OF SOLUTIONS TO THE
GROSS-PITAEVSKII HIERARCHY". However I do not really know much about the many body system problem in general. May I ask what should I read to understand the general context of their paper and other related topics? I briefly searched on arxiv and found there are quite a few (+30) papers on this topic, but they all seem rather dense. So I do not really know where to start. I am also trying to read Erdos, Schlein, H-T Yau's paper on this topic, but I found myself getting lost after a while as I do not really have enough background. I know basic quantum mechanics and basic PDE, and it seems these are vastly insufficient to understand the huge topic. 


I am reading Tao's article (<https://terrytao.wordpress.com/2009/11/26/from-bose-einstein-condensates-to-the-nonlinear-schrodinger-equation/#more-3135>) and I found it really helpful. However, I am rather lost with questions like "What are the open questions in this topic?" "Why these questions are important?" "Does physicists care about these results?" "What is a meaningful improvement of ths paper?", etc. I also found this phenomenon that we understand the mathematical statement but having poor insight of its physical background (or the real motivation behind the work) is quite common in my study group. So I venture to ask. 



What to read for many-body problems in 3D Schrodinger equation
Mean field theory is one of the most active subject concerning many body systems, and the papers you mentioned fit in this context. I think you should read this review by [Golse](http://arxiv.org/abs/1301.5494). However there are at least four different approaches to the problem. One, called coherent states method, introduced by Hepp and developed by many (especially Ginibre and Velo and recently Rodnianski and Schlein); another are the BBGKY hierarchies (look at the Golse review and also the references you already mentioned); there are also works by Pickl; and finally a method using semiclassical analysis in infinite dimensions by Ammari and Nier. I am not allowed to post all the links, sorry. However they should constitute a quite large and clarifying amount of literature on the subject, if you look for them.


