Particle in a box

An alternative view of the electronic band structure of solids is to consider the electron waves in a periodic crystalline potential. The starting point for this approach is the free electron model for metals. In this model a metallic solid is considered as consisting of a close packed lattice of positive cations surrounded by an electron sea or cloud formed from the ionization of the outer shell (valence) electrons.

we can then treat the valence electrons as if they were a gas inside a container and use classical kinetic gas theory. This works best for the electropositive metals of Groups I and II as well as aluminium (the so called free electron metals) and can explain many of the fundamental properties of metals such as high electrical and thermal conductivities, optical opacity, reflectivity, ductility and alloying properties.

The free valence electrons are assumed to be constrained within a potential well which essentially stops them from leaving the metal - the particle in a box model.


Nanoscale science and technology, Wiley, 2006





In physics, the particle in a box (also known as the infinite potential well or the infinite square well) is a problem consisting a single particle inside of an infinitely deep potential well, from which it cannot escape, and which loses no energy when it collides with the walls of the box. In classical mechanics, the solution to the problem is trivial: The particle moves in a straight line, always at the same speed, until it reflects from a wall.

The problem becomes very interesting when one attempts a quantum-mechanical solution, since many fundamental quantum mechanical concepts need to be introduced in order to find the solution. Nevertheless, it remains a very simple and solvable problem.


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