Abstract: In the paper, a class of Schrödinger equation with harmonic Potential, which concerns Bose-Einstin condensates, is investigated. Now that the equation of Bose-einstin condensates describes lot of phenomena, that we research it has special significance. With the help of using energy conservative law and quality conservative law as well as knowledge of vector analysis, integral and differential inequality, we prove that the solution to the Cauchy's problem will blow up in finite time in case initial value satisfy with some conditions. As the equation in the paper is more general, we have got extensive conclusion, by means of which we may deeply understand the aggregative phenomena on energy and quality.