Fourier Grid Hamiltonian Method Research Articles

Complex-scaling Fourier-grid Hamiltonian method. III. Oscillatory behavior of complex quasienergies and the stability of negative ions in very intense laser fields.

A complex-scaling Fourier-grid Hamiltonian (CSFGH) method in momentum representation along with Floquet formalism is presented and applied to the nonperturbative treatment of the complex quasienergies of a one-dimensional-model negative chlorine ion in an ArF excimer-laser field. The CSFGH method leads to a simple and highly efficient variational procedure for accurate determination of resonance states, without the need of using an ${\mathit{L}}^{2}$-basis-function expansion. A variety of laser intensities are considered covering those from perturbative to very intense laser fields, and the stability of the ion is investigated under realistic experimental conditions. Oscillatory structures of the photodetachment rate as a function of field strength are found in our study, revealing that the decreasing of the detachment rate (or the so-called ``stabilization'' or ``suppression-of-ionization'' phenomenon) may not necessarily be a monotonic behavior. Physical insight into this interesting feature is explored in the Kramers-Henneberger frame, and the feasibility for the experimental observation of the oscillatory behavior of the negative ions is also discussed.

Localized quantum states on and above the top of a barrier

The quantum states of a particle moving in a symmetric double-well potential (SDW) both in the presence and absence of a constant electric field are investigated within the framework of a Fourier grid Hamiltonian method. It is shown that a few states, with energies close to or above the energy at the barrier top, are strongly localized within the width of the barrier. Comments are made on the nature of these states.

Two computer programs for solving the Schrödinger equation for bound-state eigenvalues and eigenfunctions using the Fourier grid Hamiltonian method

Two computer programs (FGHEVEN and FGHFFT) for solving the one-dimensional Schrödinger equation for bound-state eigenvalues and eigenfunctions are presented. Both computer programs are based on the Fourier grid Hamiltonian method (J. Chem. Phys. 91 (1989) 3571). The method is exceptionally simple and robust. It relies on using the momentum representation for the kinetic energy operator and the coordinate representation for the potential energy. The first computer program (FGHEVEN) is based on an explicit (very simple) expression for the Hamiltonian matrix. The eigenvalues of this matrix give the required bound-state energies and the eigenvectors yield directly the eigenfunctions evaluated on the regularly spaced grid points. In this paper the theory has been slightly extended to encompass the situation where an even number of grid points is used. The second program (FGHFFT) is based on a complimentary theory which makes use of the discrete fast Fourier transform technique to evaluate the Hamiltonian matrix. The programs are self-contained and include subroutines to find the eigenvalues and eigenvectors needed.

Complex quasivibrational energy formalism for intense-field multiphoton and above-threshold dissociation: Complex-scaling Fourier-grid Hamiltonian method

We present a new complex-scaling Fourier-grid Hamiltonian (CSFGH) method for accurate and efficient determination of laser-induced (multichannel) molecular resonance states without the use of basis set expansions. The method requires neither the computation of potential matrix elements nor the imposition of boundary conditions, and the eigenvectors provide directly the values of the resonance wave functions at the space grid points. The procedure is particularly valuable for excited-state problems where basis set expansion methods face the challenge. The simplicity and usefulness of the CSFGH method is demonstrated by a case study of the intensity-dependent complex quasivibrational energy eigenvalues (ER, −Γ/2) and eigenvectors associated with multiphoton and above-threshold dissociation of H+2 ions in the presence of intense laser fields (I=1012–1014 W/cm2 ).

The complex-scaling fourier-grid Hamiltonian method for resonance state problems

We present a new complex scaling method for the study of resonance eigenstates without the use of basis set expansions. The procedure does not require the computation of potential matrix elements; the eigenvectors provide directly the values of the resonance wave functions at the space grid points. The simplicity, efficiency, and reliability of the method is illustrated by a case study of the tunneling in an anharmonic oscillator.

The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions

A new method for the calculation of bound state eigenvalues and eigenfunctions of the Schrödinger equation is presented. The Fourier grid Hamiltonian method is derived from the discrete Fourier transform algorithm. Its implementation and use is extremely simple, requiring the evaluation of the potential only at certain grid points and yielding directly the amplitude of the eigenfunctions at the same grid points.