In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is...

atom in a spherical cavity with Dirichlet boundary conditions The particle in a one-dimensional lattice (periodic potential) The particle in a one-dimensional...

a ring particle in a spherically symmetric potential quantum harmonic oscillator hydrogen atom ring wave guide particle in a one-dimensional lattice (periodic...

what their signs are or how limited their sizes are. For a particle in a one-dimensional lattice, like the Kronig–Penney model, it is possible to calculate...

example: a rigid regular, crystalline (not amorphous) lattice is composed of N particles. These particles may be atoms or molecules. N is a large number...

A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If...

worked out in a specific situation, see the article Particle in a one-dimensional lattice (periodic potential). Bloch's theorem — For electrons in a perfect...

oscillator Hydrogen atom or hydrogen-like atom Ring wave guide Particle in a one-dimensional lattice (periodic potential) Hydrogen molecular ion Holstein–Herring...

form of the particle in a box model considers a one-dimensional system. Here, the particle may only move backwards and forwards along a straight line...

dimension. In 4D this is D4 lattice; and E8 lattice in 8-dimension. The implementation of these high dimensional periodic boundary conditions is equivalent...

This state is either a band-edge state or a surface state in the band gap(see, Particle in a one-dimensional lattice, Particle in a box). Numerical calculations...

particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles...

transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition...

consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice. Due to its particulate...

This is a list of known and hypothesized particles. Elementary particles are particles with no measurable internal structure; that is, it is unknown whether...

particles bombard the lattice, creating collision cascades and additional vacancies, which migrate towards sinks. The main effect of irradiation in a...

symmetry, lattice packings are easier to classify than non-lattice ones. Periodic lattices always have well-defined densities. In three-dimensional Euclidean...

a 3×1018-dimensional vector space—one dimension for each coordinate (x, y, z) of each particle. Directly and straightforwardly trying to solve such a...

lattice, forming a lattice path. In a simple symmetric random walk on a locally finite lattice, the probabilities of the location jumping to each one...

particle}}}}} In these formulas, r particle {\displaystyle r_{\text{particle}}\,} is the particle radius, γ particle-matrix {\displaystyle...

describing free propagation of the electron-hole pair as a composite particle in the crystalline lattice in agreement with the Bloch theorem. The exciton energy...

A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited...

model is a two-dimensional model of fluid particle interactions. In this model, the lattice is square, and the particles travel independently at a unit speed...

group. The notation of a harmonic oscillator can be extended to a one-dimensional lattice of many particles. Consider a one-dimensional quantum mechanical...

Sanders, Jerome C. (Apr 2010). "Dimer of two bosons in a one-dimensional optical lattice". Phys. Rev. A. 81 (4): 043609. arXiv:1004.5118. Bibcode:2010PhRvA...

provide a possible platform for direct tuning of wavelength in optical lattice systems. Continuous control of the periodicity of a one-dimensional optical...

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called...

point, so that a one-dimensional or two-dimensional scalar does not have a well defined average value. If the field is an angle, θ, as it is in the Mexican...

derivation: a charged quantum particle in a two-dimensional square lattice, with a lattice spacing a {\displaystyle a} , is described by a periodic Schrödinger...

A Peierls transition or Peierls distortion is a distortion of the periodic lattice of a one-dimensional crystal. Atomic positions oscillate, so that the...