Klein Paradox for the Klein-Gordon Equation

1959 ◽  
Vol 27 (5) ◽  
pp. 355-358 ◽  
Author(s):  
Rolf G. Winter
Keyword(s):  
Gordon Equation ◽  
Klein Paradox ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Klein paradox for bosons, wave packets and negative tunnelling times

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
X. Gutiérrez de la Cal ◽  
M. Alkhateeb ◽  
M. Pons ◽  
A. Matzkin ◽  
D. Sokolovski
Keyword(s):  
Pair Production ◽  
Gordon Equation ◽  
Wave Packets ◽  
Transmission Mechanism ◽  
Multiple Reflections ◽  
Klein Paradox ◽  
Klein Gordon ◽  
Rectangular Barrier ◽  
Klein Gordon Equation

Abstract We analyse a little known aspect of the Klein paradox. A Klein–Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein–Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier’s height is enhanced yet remains finite.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

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