In this paper, the q Euclidean space and the q deformed harmonic oscil
lators in this space are described by an algebraic system. In this sys
tem we can define the raising (creation) and the lowering (annihilatio
n) operators. These operators form a quantum hyperplane and the corres
ponding covariant q partial derivatives. From the viewpoint of this qu
antum hyperplane, the operator q Schrodinger equation and the explanat
ion of its solutions are discussed. In addition, some related q implic
ate-order structures are presented.