Bloch wave

The states in this basis are called Bloch waves.

The former proves that the Bloch waves are energy eigenstates.

In a crystal lattice, the wavefunctions and are simply Bloch waves.

Since the potential is periodic deep inside the crystal the electronic wave functions must be Bloch waves here.

Since , that proves that the Bloch wave has the expected form.

Bloch wave functions describe the electronic states in a periodic crystal lattice.

It is an extended Bloch wave within the crystal with an exponentially decaying tail outside the surface.

See Bloch wave for further details.

His doctoral thesis established the quantum theory of solids, using Bloch waves to describe the electrons.

In contrast, a shallow potential depth, Bloch waves as well as quantum tunneling become of importance.

Bloch wave homogenization and spectral asymptotic analysis, J. Math.

The Schrödinger equation is solved for the crystal, which has Bloch waves as solutions:

Bloch wave decomposition in the homogenization of periodically perforated media, Indiana Univ.

Bloch wave - MoM is a technique for determining the band structure of triply-periodic electromagnetic media such as photonic crystals.

The eigenfunctions of these Hamiltonians are Bloch waves which are modulated plane waves.

In condensed matter physics an energy eigenfunction for a mobile charge carrier in a crystal can be expressed as a Bloch wave:

A further generalization appears in the context of Bloch waves and Floquet theory, which govern the solution of various periodic differential equations.

This technique uses the method of moments (MoM) in combination with a Bloch wave expansion of the electromagnetic field in the structure.

Examples of propagating natural modes would include waveguide modes, optical fiber modes, solitons and Bloch waves.

Each Bloch wave is (by construction) an eigenstate of the Hamiltonian, and also an eigenstate of all the translation operators.

Using the Fourier transform analysis, a spatially localized wave function for the m-th energy band can be constructed from multiple Bloch waves:

For the theorem named after Felix Bloch on wave functions of a particle in a periodic potential, see Bloch wave.

At the band edge, conduction band Bloch waves exhibit s-like symmetry, whole valence band states are p-like (3-fold degenerate without spin).

This is because these states cannot be described with periodic Bloch waves due to the change in electron potential energy caused by the missing ion cores just outside of the surface.

The ansatz is the special case of electron waves in a periodic crystal lattice using Bloch waves as treated generally in the dynamical theory of diffraction.