Quantum confinement model, description

In this section, a return will be made to the concept of quantum confinement of carriers in a solid, and the concept used to derive a more detailed description of the electronic band stmcture in a low-dimensional solid. This description, although more elaborate than that just given above, is indeed more powerful and will catch the general physics of a solid when its dimensions shrink, one by one, down to a few nanometers. Initially, an elementary model of the behavior of electrons in a bulk solid will be considered, and this will then be adapted to the case of confined carriers. 

Band theory provides a picture of electron distribution in crystalline solids. The theory is based on nearly-free-electron models, which distinguish between conductors, insulators and semi-conductors. These models have much in common with the description of electrons confined in compressed atoms. The distinction between different types of condensed matter could, in principle, therefore also be related to quantum potential. This conjecture has never been followed up by theoretical analysis, and further discussion, which follows, is purely speculative. 

The electrons in an atom also have an intrinsic angular momentum in addition to their orbital angular momentum about the nucleus. This is called the electron spin or sometimes just referred to as spin. Even an electron in the / = 0 orbital that has zero angular momentum will have an intrinsic spin. The intrinsic spin of the electron is not a classical mechanical effect hence, it is not a correct picture to view the electron spinning about one of its axes, as the classical mechanical picture would indicate. The term spin is more of a name for this phenomenon rather than an actual description of the electron. Though the intrinsic spin of the electron is real, there is no example in the macroscopic world to form a visual model. The electron spin arises naturally when relativistic mechanics is combined with quantum mechanics. Since this text is confined to quantum mechanics, the concept of electron spin must be introduced as a hypothesis. 

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