Tunneling Effect

Tunneling effect Quantum tunnelling Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. It can be generalized to other types of classically-forbidden transitions as well. Consider rolling a ball up a hill. If the ball is not given enough velocity, then it will not roll over the hill. This scenario makes sense from the standpoint of classical mechanics, but is an inapplicable restriction in quantum mechanics simply because quantum mechanical objects do not behave like classical objects such as balls. On a quantum scale, objects exhibit wavelike behavior. For a quantum particle moving against a potential energy "hill", the wave function describing the particle can extend to the other side of the hill. This wave represents the probability of finding the particle in a certain location, meaning that the particle has the possibility of being detected on the other side of the hill. This behavior is called tunnelling; it is as if the particle has 'dug' through the potential hill. As this is a quantum and non-classical effect, it can generally only be seen in nanoscopic phenomena — where the wave behavior of particles is more pronounced. Availability of states is necessary for tunneling to occur. In the above example, the quantum mechanical ball will not appear inside the hill because there is no available "space" for it to exist, but it can tunnel to the other side of the hill, where there is free space. Analogously, a particle can tunnel through the barrier, but unless there are states available within the barrier, the particle can only tunnel to the other side of the barrier. The wavefunction describing a particle only expresses the probability of finding the particle at a location assuming a free state exists.

Contents • • • •

1 History and consequences 2 Semiclassical calculation 3 See also 4 References

History and consequences In the early 1900s, radioactive materials were known to have characteristic exponential decay rates or half lives. At the same time, radiation emissions were known to have certain characteristic energies. By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunnelling. Classically, the particle is confined to the nucleus

because of the high energy requirement to escape the very strong potential. Under this system, it takes an enormous amount of energy to pull apart the nucleus. In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape. Gamow solved a model potential for the nucleus and derived a relationship between the half-life of the particle and the energy of the emission. Alpha decay via tunnelling was also solved concurrently by Ronald Gurney and Edward Condon. Shortly thereafter, both groups considered whether particles could also tunnel into the nucleus. After attending a seminar by Gamow, Max Born recognized the generality of quantummechanical tunnelling. He realised that tunnelling phenomena was not restricted to nuclear physics, but was a general result of quantum mechanics that applies to many different systems. Today the theory of tunnelling is even applied to