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

A Hamiltonian coupling identification (HCI) technique is introduced to reveal the independent and cooperative roles of Hamiltonian matrix elements in determining the bound-state energies of quantum systems. The HCI technique operates by encoding each Hamiltonian matrix element with a unique modulation signal, producing a nonlinear signature in the energy eigenvalues that may be decoded to reveal the contributing coupling structure in the Hamiltonian. The HCI technique is capable of exploring the roles of Hamiltonian coupling structure within and beyond the convergence limits of standard perturbation theory expansions. The flexibility residing in the encoding and decoding processes may be exploited to tailor the analysis to meet the desired degree of sought-after information about the Hamiltonian coupling structure. HCI, based on a Fourier encoding and decoding scheme, is illustrated by extracting information on the role of coupling interactions in the potential matrix elements of several simple model systems.