Klein paradox

The Klein paradox is a theoretical phenomenon in quantum mechanics where a relativistic particle, like an electron, encountering a potential barrier of infinite height would not be reflected as expected in classical physics. Instead, it would tunnel through the barrier with a probability of 1, and even appear on the other side with negative energy. This paradox arises from the relativistic wave equations, specifically the Dirac equation, which describes the behavior of spin-½ particles.1

The paradox highlights a counterintuitive aspect of quantum mechanics, suggesting that particles can pass through seemingly impenetrable barriers and even exhibit negative energy states. While the paradox itself is a theoretical construct, it has spurred deeper investigations into the nature of quantum fields and relativistic effects. The concept of tunneling, where particles can pass through energy barriers, is a well-established quantum mechanical phenomenon with practical applications, though the specific "Klein paradox" scenario with infinite barriers and negative energy is a theoretical extreme.2341