Article citationsMore>>
Delgado, F., Muga, J.G., Ruschhaupt, A., García-Calderón, G. and Villavicencio, J. (2003) Tunneling Dynamics in Relativistic and Nonrelativistic Wave Equations. Physical Review A, 68, Article ID: 032101.
https://doi.org/10.1103/physreva.68.032101
has been cited by the following article:
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TITLE:
Dispersion Relations in Diffraction in Time
AUTHORS:
Salvador Godoy, Karen Villa
KEYWORDS:
Diffraction in Time, Dispersion Relations, Hilbert Transforms
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.7,
July
26,
2024
ABSTRACT: In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity,
g(
x
′
)=±Sgn(
x
′
)g(
x
′
)
, which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.