Quantum propagator for a general time-dependent quadratic Hamiltonian: Application to interacting oscillators in external fields

Abstract In this paper, we find the quantum propagator for a general time-dependent quadratic Hamiltonian. The method is based on properties of and fact that fulfills two independent partial differential equations originating from Heisenberg positions momenta. As an application method, linear chain interacting oscillators both periodic Dirichlet boundary conditions. state excitation propagation along harmonic in absence presence external classical source studied discussed. location first maxima probability amplitude P ( n , τ ) straight line )-plane, indicating constant speed chain.