Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8404Research ArticleIonization Amplitude Extraction from the Solution of the Time-Dependent Schr¨odinger Equation by Means of the Probability Amplitude Surface FluxSerovV VDepartment of Theoretical Physicsvladislav_serov@mail.ruSergeevaT ADepartment of Theoretical Physicssergeevata.ssu@gmail.comVinitskyS IBogoliubov Laboratory of Theoretical Physicsvinitsky@theor.jinr.ruSaratov State UniversityJoint Institute for Nuclear Research15022014241943008092016Copyright © 2014,2014We have developed a new method for the obtaining of the amplitudes of ionization of atoms and molecules by the strong time-dependent field from the solution of the time-dependent Schr¨odinger equation (TDSE). The method is based upon the conjunction of the two approximate approaches for the amplitude computation that have been proposed earlier. One of these approaches makes it possible to confine oneself to evaluate the wavefunction on the small space region while the other allows to do it for the small time interval. The method that is being suggested here combines these advantages, so it enables to extract ionization amplitudes by means of solving the TDSE both on the small space region and for the time interval not exceeding the external ionizing field duration. It is shown that the method we are proposing yields results more exact compared to the precessors as well as does not suffers from their peculiar drawbacks. These statements validity has been demonstrated by the example of the one-dimensional problem with the model potential. The correct boundary conditions were provided by means of the exterior complex scaling. In the future the method might be utilized for the aid of the solution of much more complicated problems.ionizationlaser pulsestime-dependent Schr¨odinger equationwave functionemitted electrons spectrumnumerical methodsионизациялазерные импульсывременное уравнение Шрёдингераволновая функцияспектр испущенных электроновчисленные методы