History and Related Equations
The concept of the Bloch state was developed by Felix Bloch in 1928, to describe the conduction of electrons in crystalline solids. The same underlying mathematics, however, was also discovered independently several times: by George William Hill (1877), Gaston Floquet (1883), and Alexander Lyapunov (1892). As a result, a variety of nomenclatures are common: applied to ordinary differential equations, it is called Floquet theory (or occasionally the Lyapunov–Floquet theorem). Various one-dimensional periodic potential equations have special names, for example, Hill's equation:
where the are constants. Hill's equation is very general, as the θ-related terms may be viewed as a Fourier series expansion of a periodic potential. Other much studied periodic one-dimensional equations are the Kronig–Penney model and Mathieu's equation.
Read more about this topic: Bloch Wave
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