Adiabatic switching in time-dependent fourier grid Hamiltonian method: some test cases

Abstract

Adiabatically switched time-dependent Fourier grid Hamiltonian methods in one and many dimensions are proposed and tested. The method encounters no difficulty even in the presence of tunneling, level crossings and can handle fairly large changes or distortions in the Hamiltonian. The specific eigenstate is obtained as the limit of a continuous succession of eigenstates of a slowly changing H(t), the T = 0 and T = T (large) limits of which are well defined. Important features of the method are analysed with particular reference to the adiabatic passage of an eigenstate of (a) a harmonic oscillator to the corresponding eigenstate of a forced harmonic oscillator, (b) a harmonic oscillator to an appropriate eigenstate of a symmetric or an asymmetric double well Hamiltonian, (c) a Morse oscillator to that of a double well Hamiltonian, and (d) a two-dimensional harmonic oscillator to the appropriate eigenstate of a Henon-Heiles system.