The geometrical formulation of Hamiltonian mechanics

Abstract

The aim of this thesis is to explain some of the connections between mechanics ( Specially Hamiltonian Mechanics) and Differential Geometry. And to shed the light on formulation of classical mechanics in tenns of Symplectic Geometry. Also to show how the standard Hilbert space formulate the quantum mechanics ( the time evolution of a state is controlled by the equation ih%=7{(z )1;/(z )). Here we also apply the fibre bundle approach to the description of observables.