The Klein Paradox in the Phase Space Quantum Mechanics

Abdulaziz D Alhaidari, A. Al‐Hajry, Ahmad Umar +4 more

Bernd Thaller

T Shivalingaswamy, Nagalakshmi A. Rao, B. A. Kagali

In this article, we discuss a paradoxical result that exists for positive energy Klein-Gordon particles. It may be called “Klein paradox” of another kind. We have shown its existence in one, two and three dimensions. The paradox seems to indicate the limitations of the single particle Klein-Gordon equation in the presence of strong potentials.

Chuting Xu, Y. J. Li

It is well known that, Klein paradox is one of the most exotic and counterintuitive consequences of quantum theory. Nevertheless, many discussions about the Klein paradox are based upon single-particle Dirac equation in quantum mechanics rather than quantum field method. By using the path integral formalism, we evaluate the reflection and transmission coefficients up to the lowest order for the electron scattering by the finite square barrier potential. Within the context of assuming the step potential is the limiting case of the finite square barrier potential, we explain the Klein paradox that is caused by the ill-definition of the step potential.

CHRISTOF WETTERICH

Manik Kapil, Bikash K. Behera, Prasanta Kumar Panigrahi

The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the discovery of pions and other subatomic particles. The equation leads to the development of Dirac equation and hence quantum field theory. It shows interesting quantum relativistic phenomena like Klein Paradox and "Zitterbewegung", a rapid vibrating movement of quantum relativistic particles. The simulation of such quantum equations initially motivated Feynman to propose the idea of quantum computation. While many such simulations have been done till date in various physical setups, this is the first time a digital quantum simulation of Klein Gordon equation is proposed on IBM's quantum computer. Here we simulate the time-dependent Klein Gordon equation in a barrier potential and clearly observe the tunnelling of the particle and anti-particle through a strong potential claiming Klein Paradox. The simulation technique used here inspires the quantum computing community for further studying Klein Gordon equation and applying it to more complicated quantum mechanical systems.