Hamilton-Jacobi quantization of the finite dimensional systems with constraints

The Hamiltonian treatment of constrained systems in Gülers formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a Jacobi system. The main aim of this paper is to investigate the quantization of the finite dimensional systems with constraints using the canonical formalism introduced by Güler. This approach is applied for two systems with constraints and the results are in agreement with those obtained by Dirac’s canonical quatization method and path integral quantization method.