In quantum mechanics, a smooth barrier refers to a situation where a particle encounters a barrier or potential energy region that changes gradually and smoothly rather than abruptly. This concept is often encountered in the study of particle behaviour, particularly in scenarios involving wave-like properties.

Imagine you have a particle, like an electron, and it's moving towards a region with a potential energy barrier. This barrier might represent some kind of obstacle or energy barrier that the particle needs to overcome.

In classical physics, when a particle encounters a barrier, it can be thought of as a simple "yes" or "no" situation. Either the particle has enough energy to overcome the barrier and continue moving, or it doesn't and gets stopped completely.

However, in quantum mechanics, particles also exhibit wave-like behaviour. When a quantum particle encounters a smooth barrier, it doesn't simply stop like a classical particle would. Instead, its wave function (which describes the probability distribution of the particle's position) can extend into the barrier region, even if the probability of finding the particle there is low.

This phenomenon is a result of the wave-particle duality inherent in quantum mechanics. The particle is described by a wave function that spreads out and interacts with the barrier, allowing for the possibility of "tunneling" through the barrier even if the particle's energy is lower than the barrier's height.

In summary, a smooth barrier in quantum mechanics refers to a potential energy barrier that changes gradually and allows for the possibility of wave-like behaviour, such as tunneling, where particles can penetrate the barrier even if they don't have enough classical energy to overcome it. This concept challenges our classical intuition and is a fundamental aspect of the quantum world.

A smooth curved barrier can be assumed to be the combination of large number of square barrier of indefinitely small width and of varying height.

This note is a part of the Physics Repository.

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