[Zhong-Qi, M. A.] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; [Yang, C. N.] Tsinghua Univ, Inst Adv Study, Beijing 100084, Peoples R China
; [Yang, C. N.] Chinese Univ Hong Kong, Inst Theoret Phys, Hong Kong, Hong Kong, Peoples R China
In these two papers, we solve the.. body 1D harmonically trapped spinless Boson problem with repulsive delta function interaction in the limit N -> infinity. The general theory is given in paper I and the numerical solutions will be given in paper II.