Hamiltonian formulation of quantum mechanics with semiclassical implications

An exact Hamiltonian formulation of nonrelativistic quantum mechanics that simplifies to ordinary classical mechanics as Latin small letter h with stroke0 is presented. The theory allows one to treat a quantum system as the corresponding classical system mechanically connected to an infinite number of additional classical degrees of freedom. The onset of quantum effects such as tunneling and interference results from the mechanical interactions between the different parts of the overall infinite system. The formalism is applied to the one-dimensional motion of a particle in a symmetric double well. It is shown that the tunneling in that system involves multidimensional classical motion that circumvents the barrier.