Electron Scattering at a Potential Temporal Step Discontinuity
- URL: http://arxiv.org/abs/2307.08111v3
- Date: Tue, 20 Feb 2024 10:07:45 GMT
- Title: Electron Scattering at a Potential Temporal Step Discontinuity
- Authors: Furkan Ok, Amir Bahrami, Christophe Caloz
- Abstract summary: We show that the Schrodinger equation cannot account for scattering in this problem.
We derive the scattering probabilities, of later forward and backward nature, with the later-backward wave being a relativistic effect.
- Score: 0.27624021966289597
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We solve the problem of electron scattering at a potential temporal step
discontinuity. We show that the Schrodinger equation cannot account for
scattering in this problem, necessitating resort to the Dirac equation, and
that breaking gauge symmetry requires a vector potential, a scalar potential
inducing only Aharonov-Bohm type energy transitions. We derive the scattering
probabilities, of later forward and backward nature, with the later-backward
wave being a relativistic effect, and compare the results with those for the
spatial step and classical electromagnetic counterparts of the problem. Given
the unrealizability of an infinitely sharp temporal discontinuity - which is of
the same nature as its spatial counterpart! - we also provide solutions for a
smooth potential step and demonstrate that the same physics as for the
infinitely sharp case is obtained when the duration of the potential transition
is sufficiently smaller than the de Broglie period of the electron (or deeply
sub-period).
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