Abstarct: The study of quantum systems under the influence of a gravitational field has been developing research field. Along this researches we investigate effect of behavior of quantum particles in the presence of gravitational field. An interesting point is that the gravitational field creates curved space time around so for analyzing behavior of particles in the presence of gravitational field we should investigate interaction of particles with the curved space time. In order to discuss on such phenomena, motion equations would be specified in terms of properties of particles for example to study spinless nonrelativistic particles it should be used Schrödinger equitation. Therefore motion equations would be formulated in the curved space time since descxription of generalized equations will be presented. So different curved space time such as cosmic string, spinning cosmic string and Friedmann- Robertson- Walker space times will be introduced and finally we study effects of them on the physical systems.