Related Experiment Video
Updated: Aug 17, 2026

Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol
Published on: December 20, 2016
Exponential decay properties of Wannier functions and related quantities
1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849, USA.
Abstract:
The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of nonorthonormal Wannier-like functions.
Related Concept Videos
The de Broglie Wavelength
Exponential and Sinusoidal Signals
Introduction to Exponential Functions
Improper Integrals: Infinite Intervals
Bessel Function of Order Zero
Exponential Functions with Base e

