Abstract
A new method was developed to solve the Dirac equation and used to find analytical solutions for time-dependent electromagnetic fields that translate a given Dirac spinor along any desired trajectory in the $x\text{\ensuremath{-}}y$ plane without distortion. As is well known, negative energy solutions describing antiparticles play a prominent role in the Dirac theory of the electron, and a separation of the part of the wave function describing only electrons from the full solutions often needs to be done. Here, we clarify how the aforementioned separation is done, which is not clear in our recent publication [Campos and Cabrera, Phys. Rev. Research 2, 013051 (2020)].
Highlights
In the recent Comment, the authors state that “physical interpretation of the results is incomplete. . .” The reason stated by the authors is that “The Dirac equation in the presence of any time-dependent electromagnetic field is not an equation describing just the evolution of a wave packet of an electron
In order to use a solution of the Dirac equation to describe the motion of the electron wave packets, one must be sure that the part describing the motion of electrons has been separated from the full solution
In order to better illustrate that the separation between electronic and positronic states has been done, we numerically solve the Dirac equation using an adapted version of the code given in Ref. [6] for the vector potential given by Eqs. (17) of Ref. [1] for the case of an elliptical trajectory with an initial state given by Eq (15) of Ref. [1] for t = 0, which has the form of a spin-down, positive energy spinor
Summary
In the recent Comment, the authors state that “physical interpretation of the results (given in Refs. [1,2]) is incomplete. . .” The reason stated by the authors is that “The Dirac equation in the presence of any time-dependent electromagnetic field is not an equation describing just the evolution of a wave packet of an electron. In the recent Comment, the authors state that “physical interpretation of the results . .” The reason stated by the authors is that “The Dirac equation in the presence of any time-dependent electromagnetic field is not an equation describing just the evolution of a wave packet of an electron.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
