Variational Iterative Time Dependent Method for Eigenvalues and Eigenfunctions of the Hamiltonian

Short time information on the time evolution of wave packets is combined with the variational theorem to determine eigenvalues and eigenfunctions. As in the Filter Diagonalization Method the input that is needed is a correlation function and its time derivative. The method is iterative and convergent. The time interval needed is short, for example, the determination of tunneling splitting energies ΔE is obtained in a time interval which is substantially shorter than the Fourier time 2πℏ/ΔE. The method is applied to some model problems including determining the ground tunneling state in a quartic double well potential using numerically exact short time results obtained from the semiclassical initial value representation series of the exact propagator. This is another example in which tunneling is obtained using only coherent classical paths. Implications of the method for ab initio computation of molecular electronic energies is discussed.