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An eigenstate chosen to transform under a lattice translation by a one-dimensional phase character, equivalently written as a plane wave times a lattice-periodic function.
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Under lattice periodicity, eigenstates can be chosen to transform by lattice-translation characters and therefore have Bloch form.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solidsThis is an authored directed relation from the source endpoint to the target endpoint.
Lattice translations act on one-particle states by commuting unitary operators. A Bloch state transforms in a one-dimensional character of that Abelian translation group, labeled by crystal momentum modulo the reciprocal lattice.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-group-representationwp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solidsEach relation below starts at this concept.
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