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Schrödinger equation

About: Schrödinger equation is a(n) research topic. Over the lifetime, 25550 publication(s) have been published within this topic receiving 535429 citation(s). more


Journal ArticleDOI: 10.1103/PHYSREVLETT.52.997
Erich Runge1, E. K. U. Gross1Institutions (1)
Abstract: The response of an interacting many-particle system to a time-dependent external field can usually be treated within linear response theory. Due to rapid experimental progress in the field of laser physics, however, ultra-short laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse one observes a wealth of new phenomena [1] which cannot be explained by traditional perturbation theory. The non-perturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. In principle, it requires a full solution of the time-dependent Schrodinger equation for the interacting many-body system, which is an exceedingly difficult task. In view of the success of density functional methods in the treatment of stationary many-body systems and in view of their numerical simplicity, a time-dependent version of density functional theory appears highly desirable, both within and beyond the regime of linear response. more

6,210 Citations

Journal ArticleDOI: 10.1063/1.466059
Abstract: In this paper, potential‐dependent transformations are used to transform the four‐component Dirac Hamiltonian to effective two‐component regular Hamiltonians. To zeroth order, the expansions give second order differential equations (just like the Schrodinger equation), which already contain the most important relativistic effects, including spin–orbit coupling. One of the zero order Hamiltonians is identical to the one obtained earlier by Chang, Pelissier, and Durand [Phys. Scr. 34, 394 (1986)]. Self‐consistent all‐electron and frozen‐core calculations are performed as well as first order perturbation calculations for the case of the uranium atom using these Hamiltonians. They give very accurate results, especially for the one‐electron energies and densities of the valence orbitals. more

Topics: Dirac equation (53%), Relativistic quantum chemistry (53%), Schrödinger equation (52%) more

3,208 Citations

Journal ArticleDOI: 10.1063/1.459170
Abstract: A method is proposed for carrying out molecular dynamics simulations of processes that involve electronic transitions. The time dependent electronic Schrodinger equation is solved self‐consistently with the classical mechanical equations of motion of the atoms. At each integration time step a decision is made whether to switch electronic states, according to probabilistic ‘‘fewest switches’’ algorithm. If a switch occurs, the component of velocity in the direction of the nonadiabatic coupling vector is adjusted to conserve energy. The procedure allows electronic transitions to occur anywhere among any number of coupled states, governed by the quantum mechanical probabilities. The method is tested against accurate quantal calculations for three one‐dimensional, two‐state models, two of which have been specifically designed to challenge any such mixed classical–quantal dynamical theory. Although there are some discrepancies, initial indications are encouraging. The model should be applicable to a wide variety of gas‐phase and condensed‐phase phenomena occurring even down to thermal energies. more

Topics: Surface hopping (57%), Electronic structure (54%), Equations of motion (51%) more

2,794 Citations

Journal ArticleDOI: 10.1016/0021-9991(82)90091-2
Michael D. Feit1, J. A. Fleck1, A Steiger1Institutions (1)
Abstract: A new computational method for determining the eigenvalues and eigenfunctions of the Schrodinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schrodinger equation. The method requires the computation of a correlation function 〈ψ( r , 0)| ψ( r , t )〉 from a numerical solution ψ( r , t ). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of ψ( r , t ) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon-Heiles potential. more

Topics: Spectral method (58%), Partial differential equation (58%), Schrödinger equation (56%) more

2,487 Citations

Open accessJournal ArticleDOI: 10.1353/AJM.1998.0039
Markus Keel1, Terence Tao1Institutions (1)
Abstract: We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n ≥ 4) and the Schrodinger equation (in dimension n ≥ 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartz-type estimates for more general dispersive equations and for the kinetic transport equation. more

Topics: Wave equation (59%), Schrödinger equation (58%), Convection–diffusion equation (55%) more

2,003 Citations

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Topic's top 5 most impactful authors

Ramazan Sever

96 papers, 2.5K citations

T. E. Simos

96 papers, 3.3K citations

Hassan Hassanabadi

54 papers, 638 citations

Rémi Carles

52 papers, 1.2K citations

Francisco M. Fernández

50 papers, 616 citations

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