This thesis contains five chapters. The first two are devoted to the background which consists of integration, Fourier analysis, distributions and linear operators in Hilbert spaces. The third chapter is a generalization of a work done by Albrecht-Spain in 2000. We give a shorter proof of the main theorem they proved for bounded operators and we generalize it to unbounded operators. We give a counterexample that shows that the result fails to be true for another class of operators. We also say why it does not hold. In chapters four and five, the idea is the same, that is to find classes of unbounded, real-valued Vs for which  + V is self-adjoint on D(), where  is the wave operator. Throughout these two chapters we will see how different the Laplacian and the wave operator can be.