The intrinsic quantum properties shown in electrons and atoms allow us to explode a non-classic field for the information management. Through the Stern-Gerlach device (SG), the measurement of spin via a momentum is obtained with associated probabilities due to quantum principles. This paper studies the behavior of a three-particle coupled quantum system in which a spin particle is measured by the SG apparatus while the others are not. The response of the spin-1/2 uncharged particle because of the inhomogeneous magnetic field is also analyzed introducing as well non-linear variations of the magnetic field. The system solution will be determined by specials functions according to the variation field defined and three cases with Airy, Whittaker and Heun functions will be treated and supported by different simulations using symbolic computation with Maple.