Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Solution of the Time-dependent Schrodinger Equation via Complex Quantum Trajectories

Yair Goldfarb

Published Jan 1, 2008• 2 citations
OpenAlex

Related papers

Solution of the time-dependent Schrödinger equation with a trajectory method and application to H+-H scattering

Georg Terlecki, NORBERT GRÜN, W. Scheid

Physics Letters A•Feb 1, 1982•28 citations

Enhanced tunneling through nonstationary barriers

Juan Pedro Palomares-Báez, Boris I. Ivlev, José Luis Rodríguez‐López

Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.

Physical Review A•Nov 7, 2007•12 citations

On the time-dependent solutions of the Schrödinger equation

Alejandro Palma, I. Pedraza

Progress in theoretical chemistry and physics•Jan 1, 2007•3 citations

Time-dependent Schrödinger equation admitting an exact solution

Alexander S. Chikhachev

Journal of Experimental and Theoretical Physics•Apr 1, 1995•0 citations

Trajectory method for the solution of the time-dependent Schrodinger equation in atomic physics and application to H+-H scattering

Georg Terlecki, NORBERT GRÜN, W. Scheid

A trajectory method has been developed for the solution of the one-electron Schrodinger equation in atomic scattering problems. The method is based on the fluid dynamical interpretation of the quantum mechanical probability density and current. The time evolution is described by trajectories of particles, which represent the probability distribution. The trajectories are calculated by solving classical equations of motion with forces depending on the probability density. Results are obtained for the differential and total ionisation and charge exchange cross sections for the scattering of H + on H.

Journal of Physics B Atomic and Molecular Physics•Sep 28, 1984•20 citations

Solution of time-dependent Schrödinger equation in a nontraditional Hilbert space

A. Ya. Dzyublik

Theoretical and Mathematical Physics•Apr 1, 1991•13 citations
Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.
A trajectory method has been developed for the solution of the one-electron Schrodinger equation in atomic scattering problems. The method is based on the fluid dynamical interpretation of the quantum mechanical probability density and current. The time evolution is described by trajectories of particles, which represent the probability distribution. The trajectories are calculated by solving classical equations of motion with forces depending on the probability density. Results are obtained for the differential and total ionisation and charge exchange cross sections for the scattering of H + on H.