logearav said:The wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the barrier. Why it shows an exponential decay inside the barrier? After coming out of the barrier, there is reduced probability for the particle. When there is no loss of energy after coming out of the barrier why there is reduced probability?
The tunneling effect or barrier penetrability is a quantum phenomenon where a particle is able to pass through a potential energy barrier that would be classically impossible to overcome. This effect occurs due to the wave-like nature of particles, allowing them to exist in multiple places at once and "tunnel" through the barrier.
The tunneling effect occurs when the particle's wave function extends into the barrier region, allowing for a small probability of the particle to exist on the other side of the barrier. This probability decreases exponentially with the width and height of the barrier, but it is never zero.
The tunneling effect is affected by the energy and mass of the particle, as well as the width and height of the barrier. A higher energy or smaller mass particle is more likely to tunnel through a barrier, and a wider or taller barrier reduces the chances of tunneling.
The tunneling effect has many practical applications, including in electronics and microscopy. For example, it is used in tunneling diodes and scanning tunneling microscopes to manipulate and observe materials at the atomic level.
While the tunneling effect is a fundamental phenomenon in quantum mechanics, it is not observable on a macroscopic scale. Additionally, the probability of tunneling decreases rapidly with the size and complexity of the barrier, making it difficult to control and predict in certain scenarios.