Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2007.1314.1320AjlouniAbdul-WaliJoudehBassamSalamehBelal9200779The canonical quantization of a system of free particle in a bounded volume in space, particle in a box, containing a dissipative medium, is carried out according to the Dirac method. A suitable Schrödinger equation is set up and solved for the Lagrangian representing this system. The viscous forces effects and hence the dissipation are represented clearly in the resultant wave function as will as in the energy eigenvalues.]]>Rabei, E., A.W. Ajlouni and H. Ghassib,2006Rabei, E., A.W. Ajlouni and H. Ghassib,2006Goldstein, H.,1980Rabei, E.M., T. Al-Halholy and A. Rousan,2004Griffiths, D.J.,1995Merzbacher, E.,1970Dass, T. and S. Sharma,1998Arfken, G.,1985Oldham, K.B. and J. Spanier,1974Carpintri, A. and F. Mainardi,1997