# Numerical calculation of the probabilities of quantum electron transitions between bound and free states in a multiphoton process by the method of functional integration

Alexander A. Biryukov, Samara State Transport University,

Russia.

## Abstract

Numerical calculation of the probabilities of quantum electron transitions between bound and free states in a multiphoton process by the method of functional integration.

A.A. Biryukov,

Samara State Transport University, Russia

The description of the evolution of a quantum system interacting with a high-intensity electromagnetic field (multiphoton processes) is currently an urgent and complex task. For modern technologies, it is of interest to calculate the probability of an electron transition between bound states in an atom (or molecule), as well as the transition from a bound state to a free state (ionization of an atom) under the action of an intense electromagnetic field. These are the probabilities of multiphoton processes. The method of perturbation theory, applied to these processes, has limited possibilities. Therefore, the development of a non-perturbative method for describing the evolution of an electron in these problems is relevant.

One of the promising, non-perturbative approaches to describing the evolution of quantum systems is the formalism of functional integration (integration along trajectories). In this paper, the probability of the behavior of an electron under the action of an electromagnetic field for a certain selected finite time interval is represented as an integral along the trajectories in the space of energy states. The proposed formula for probability is valid for any form of an electromagnetic field acting on an electron. This circumstance distinguishes it favorably from the description of the process by differential equations.

Since it is not possible to calculate the functional integral, and, consequently, to represent the desired probability in the form of analytical functions of the radiation parameters, a numerical method for its integration is proposed. The analysis of the plotted graphs shows that the proposed formula successfully describes the probabilities of multiphoton processes.

## Speaker

**Alexander Biryukov**
Samara State Transport University

Russia

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