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Solving Schrodinger's Equation for Low-Dimensional Nanostructures for Understanding Quantum Confinement Effects
Published in Ashish Raman, Deep Shekhar, Naveen Kumar, Sub-Micron Semiconductor Devices, 2022
The low-dimensional structures that are fabricated under size restrictions to a few nanometers are finding applications in modern technological advances. The excitations in these structures undergo a quantum confinement effect due to finite restrictions in motion along the confinement axis and infinite motion in other directions. The number of confinement directions decides whether the material structure will act as quantum well, wire, or dot. The zero-dimensional systems, however, are named as quantum cubes, parallelepipeds, cylinders, spheres (dot), etc. It is useful to calculate energy levels in such structures with infinite barrier height to understand their use in different applications. In this chapter, we will derive the energy expressions for quasi-particles under the assumptions of the infinite energy barrier for such quantum structures.
Principles of Symbolization
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
Point phenomena are assumed to have no spatial extent and are thus termed “zero-dimensional.” Examples include weather station recording devices, oil wells, and locations of nesting sites for eagles. Locations for point phenomena can be specified in either two- or three-dimensional space; for example, oil well locations are commonly defined by x and y coordinate pairs (longitude and latitude), whereas nesting sites for eagles might be defined by x, y, and z coordinates (the z coordinate would be the height of the nest above the Earth's surface).
Multidimensional Quantum Wells
Published in Zbigniew Ficek, Quantum Physics for Beginners, 2017
Notice that the energy of the particle in a quantum dot is quantized in all three directions. Because the motion of the particle is now restricted in every direction (quantum confinement), the particle has zero dimension of freedom. That is why a quantum dot is often referred to as a zero-dimensional system. Quantum dots are also regarded as artificial atoms.
Review of stability enhanced nanofluids prepared by one-step methods—heat transfer mechanism and thermo-physical properties
Published in Chemical Engineering Communications, 2023
Annie Aureen Albert, Harris Samuel D. G., Parthasarathy V.
Nanomaterials can be classified based on their dimension as (i) zero-dimensional NPs (NPs), which have all three dimensions namely length, breadth and height confined at a single point. Electron movement is confined in all three directions. (ii) One-dimensional NPs have only one dimension, either length or breadth is not in the nano range. The other two dimensions are confined within the nano regime. The electron can move freely in one direction but its movement is confined in two directions. (iii) In two-dimensional NPs, two dimensions are beyond the nano regime, only thickness is in the nanoscale. Three-dimensional NPs are hierarchical structures that consist of one or two-dimensional NPs arranged to form three-dimensional structures. The solid phase which is dispersed in NF is generally a zero-dimensional or one-dimensional NP. NPs may be classified based on their composition as metal NPs, metal oxide NPs, metal carbide or nitride NPs, carbon-based NPs and hybrid nanomaterials (Tebaldi et al. 2016).
Outer approximation algorithms for convex vector optimization problems
Published in Optimization Methods and Software, 2023
Let further be a convex set. A hyperplane given by for some is a supporting hyperplane of S if and there exists with . A convex subset is called a face of S if with and imply . A zero-dimensional face is an extreme point (or vertex) and a one-dimensional face is an edge of S. A recession direction of convex set S is said to be an extreme direction of S if is a face for some extreme point v of S, see [21, Section 18].
A groupoid approach to C*-algebras associated with λ-graph systems and continuous orbit equivalence of subshifts
Published in Dynamical Systems, 2020
Let us denote by the vertex set Define a clopen set in for by so that Put for Since is left-resolving, the restriction of to is a homeomorphism onto if . Hence is a local homeomorphism. Let be the set of all one-sided paths of : The set has the relative topology from the infinite product topology of . It is a zero-dimensional compact Hausdorff space. For with , define a subset of by where . The set is clopen and such family generate the topology of .