HARMONIC-OSCILLATORS IN Q IMPLICATE-ORDER THEORY AND ORDER STRUCTURES

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.