Plane-wave function

Knight shift in p-type PbTe has been calculated based on relativistic augmented plane wave functions [227]. 

The free motion of a mass point along a straight line x is usually described in quantum mechanics by a de Broglie plane wave function... 

As shown in the previous discussions, the free relative motion before the collision (x >> X2) can be described quantum-mechanically by either the plane wave function (22.11) or the wave packet (24.11) moving with a constant group velocity defined by (25.11). In this asymptotic region the potential V(x) along the reaction coordinate... 

The Bloch orbital can be expanded into a basis set of plane wave functions (2 " ). 

While plane wave basis sets have primarily been used for periodic systems, they can also be used for molecular species by using a supercell approach, where the molecule is placed in a sufficiently large unit cell such that it does not interact with its own image in the neighbouring cells. Placing a relatively small molecule in a large supercell to avoid self-interaction consequently requires many plane wave functions, and such cases are handled more efficiently by localized Gaussian functions. A three-dimensional periodic system, on the other hand, may be better described by a plane wave basis than with nuclear-centred basis functions. 

One can then define the s as the eigenfunctions of the non local operator under consideration e.g. in the case of the 9 /9r operator, these will be the plane wave functions ... 

Still another method to speed up evaluation of J is the Fourier-transform Coulomb (FTC) method, which replaces the evaluation of the contributions of ERls that involve three and fonr Ganssian basis functions with a numerical evaluation using a plane-wave basis set. A plane-wave function has the form where k, I, and m are con-... 

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