ADIABATIC SWITCHING IN TIME-DEPENDENT FOURIER GRID HAMILTONIAN METHOD- SOME TEST CASES

Adiabatically switched time-dependent Fourier grid Hamiltonian methods in one and many dimensions are proposed and tested. The method encoun ters 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 succ ession 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 met hod are analysed with particular reference to the adiabatic passage of an eigenstate of (a) a harmonic oscillator to the corresponding eigen state of a forced harmonic oscillator, (b) a harmonic oscillator to an appropriate eigenstate of a symmetric or an asymmetric double well Ha miltonian, (c) a Morse oscillator to that of a double well Hamiltonian , and (d) a two-dimensional harmonic oscillator to the appropriate eig enstate of a Henon-Heiles system.