Pair prediction in a static electric field

Full text: The development of the Relativistic Quantum Mechanics was held at the end of the twenties of last century aiming to describe quantum phenomena that occur at high energy scales. The first equation proposed to describe these phenomena was the Klein-Gordon equation, which was formulated in 1927 by Swedish physicist Oscar Klein and the German physicist Walter Gordon. However, the equation led to problematic outcomes, such as negative probability densities and negative energy eigenvalues, which meant a quantum system described by the Klein-Gordon equation can decay to a state energy -∞, thus freeing an infinite amount of energy. Another strange prediction of Relativistic Quantum Mechanics is the well known Klein paradox, which relates a particle on a static electric field with a potential energy much greater than the energy of the particle, and it appears that the reflection coefficient exceeds unity. This result is explained qualitatively by the pair production of particle - antiparticle in the interface potential. To solve such problems, was proposed the Second Quantization, where the Klein-Gordon scalar field is transformed into an operator can no longer be interpreted as a wave function, as in Non-Relativistic Quantum Mechanics formulated by Schroedinger. Thus, we obtain a consistent unification of quantum mechanics with special relativity, solving the problems was discussed earlier. Under the Second Quantization, you can also get a quantitative understanding of Klein's paradox, which will be the topic discussed in this work. The pair production in a static electric field provides a great analogy for a subsequent study of pair production in the event horizon of a black hole, which is known Hawking Effect. (author)