THE CONSTRUCTION OF GEL'FAND TRIPLET SPACE STRUCTURE FOR INFINITE POTENTIAL WELL SYSTEM

The Hilbert space is the space which is usually chosen as the space of state vectors. In addition, the operators of quantum mechanics act on that space. However, the Hilbert space cannot provide a proper mathematical structure to define Dirac formulation. In particular, the use of Dirac formalism on the domain of definition of an observable leads to some physical contradictions. One example arises from the Infinite Potential Well System (IPWS) which is one of the most fundamental systems of quantum mechanics. Our aim in this paper is the explicit construction of the Gel'fand triplet for the IPWS.