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...

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...

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...

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...

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...

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

thresholds are only known for certain two-dimensional lattices that can be broken up into a self-dual array, such that under a triangle-triangle transformation...

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

phases.The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. Though it is a highly simplified...

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...

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

particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension slightly for a DLA in...

This is a list of known and hypothesized microscopic particles in particle physics, condensed matter physics and cosmology. Elementary particles are particles...

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...

bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm- algorithm Monte Carlo study". Physical Review A. 94...

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

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

best-studied example is the random walk on the d-dimensional integer lattice (sometimes called the hypercubic lattice) Z d {\displaystyle \mathbb {Z} ^{d}} . If...

higher dimensions is not known. For k {\displaystyle k} -mers on a one-dimensional lattice, we have for the fraction of vertices covered, θ k = k ∫ 0 ∞ exp...

Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique which involves a set of particles moving in continuous space and...

Alexei Kitaev in 2000. The tight binding Hamiltonian of a Kitaev chain considers a one dimensional lattice with N site and spinless particles at zero temperature...

lattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystal in solid state physics. It is famous because it is one of...

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

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

generally has a density around 63.5%. A lattice arrangement (commonly called a regular arrangement) is one in which the points of the lattice form a very symmetric...

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

the one-dimensional diagram representing the path of a point particle by a two-dimensional surface representing the motion of a string. Unlike in quantum...

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