Revealing the roles of Hamiltonian coupling in bound-state quantum systems

A Hamiltonian coupling identification (HCI) technique was used to reveal the roles of the Hamiltonian matrix in determining the bound state energies of quantum systems. The presented HCI technique was based on Fourier encoding and decoding scheme. The HCI technique revealed the roles of Hamiltonian coupling structure within and beyond the convergence limits of standard perturbation theory expansions. It was found that the convergence behavior of the perturbation expansion for the eigenvalues is related to the crossing of the energy levels during modulation and the coupling structure of the potential matrix elements. The HCI procedure also provided an efficient means of determining all of the amplitudes in a single scan over the s variable.