Abstract :
Three different algorithms are proposed for studying the evolution of explicitly time-dependent Hamiltonians. In one case the propagator is constructed by making use of the Floquet states while in the other two cases, a split-operator based technique is used. Model applications to the problem of dissociation of diatoms in strong laser fields prove encouraging and our numerical experiments show that the threshold intensity of the laser field has unique relationship with the curvature of the potential of the dissociating diatoms. Adiabatically switched time-dependent split-operator based scheme is tested. This method encounters no difficulty even in the presence of tunneling or level crossings and can tackle fairly large changes or distortions in the Hamiltonian. All the eigenstates of the perturbed Hamiltonian at t=τ (large) are obtained from the corresponding eigenstates of the unperturbed Hamiltonian at t=0 as the limit of continuous succession of eigenstates of the slowly changing H(t). The viability of this method is analysed with particular reference to the adiabatic passage of eigenstates of a harmonic oscillator to the appropriate eigenstates of a symmetric double well Hamiltonian.
