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A wave function is a mathematical tool used in quantum mechanics. It is a function typically of space or momentum or spin and possibly of time that returns the probability amplitude of a position or momentum for a subatomic particle. Mathematically, it is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time.
Learn more about quantum dots from the many resources on this site, listed below. More information on Wave Function can be found here.
12 Apr 2010 | | Contributor(s):: Saumitra Raj Mehrotra, Gerhard Klimeck
In quantum mechanics the time-independent Schrodinger's equation can be solved for eigenfunctions (also called eigenstates or wave-functions) and corresponding eigenenergies (or energy levels) for a stationary physical system. The wavefunction itself can take on negative and positive values and...
15 Jun 2006 | | Contributor(s):: Gang Li, yang xu, Narayan Aluru
Compute the charge density distribution and potential variation inside a MOS structure by using a coarse-grained tight binding model
09 Oct 2007 | | Contributor(s):: Baudilio Tejerina, Jeff Reimers
Semi-empirical Molecular Orbital calculations.
Computational Nanoscience, Lecture 20: Quantum Monte Carlo, part I
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15 May 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
This lecture provides and introduction to Quantum Monte Carlo methods. We review the concept of electron correlation and introduce Variational Monte Carlo methods as an approach to going beyond the mean field approximation. We describe briefly the Slater-Jastrow expansion of the wavefunction,...
Computational Nanoscience, Lecture 4: Geometry Optimization and Seeing What You're Doing
13 Feb 2008 | | Contributor(s):: Jeffrey C Grossman, Elif Ertekin
In this lecture, we discuss various methods for finding the ground state structure of a given system by minimizing its energy. Derivative and non-derivative methods are discussed, as well as the importance of the starting guess and how to find or generate good initial structures. We also briefly...
Discussion Session 3 (Lectures 5 and 6)
09 Sep 2010 | | Contributor(s):: Supriyo Datta
ECE 656 Lecture 1: Bandstructure Review
26 Aug 2009 | | Contributor(s):: Mark Lundstrom
Outline:Bandstructure in bulk semiconductorsQuantum confinementSummary
ECE 656 Lecture 27: Scattering of Bloch Electrons
13 Nov 2009 | | Contributor(s):: Mark Lundstrom
Outline:Umklapp processesOverlap integralsADP Scattering in graphene
27 Mar 2007 | | Contributor(s):: Alexander Gavrilenko, Heng Li
Introduction to Quantum Dot Lab
31 Mar 2008 | | Contributor(s):: Sunhee Lee, Hoon Ryu, Gerhard Klimeck
The nanoHUB tool "Quantum Dot Lab" allows users to compute the quantum mechanical "particle in a box" problem for a variety of differentconfinement shapes, such as boxes, ellipsoids, disks, and pyramids. Users can explore, interactively, the energy spectrum and orbital shapes of new quantized...
Lecture 5: Electron Spin: How to rotate an electron to control the current
21 Feb 2007 | | Contributor(s):: Heng Li, Alexander Gavrilenko
Calculation of the allowed and forbidden states in a periodic potential
Periodic Potential Lab
19 Jan 2008 | | Contributor(s):: Abhijeet Paul, Junzhe Geng, Gerhard Klimeck
Solve the time independent schrodinger eqn. for arbitrary periodic potentials
Periodic Potential Lab Demonstration: Standard Kroenig-Penney Model
03 Jun 2009 | | Contributor(s):: Gerhard Klimeck, Benjamin P Haley
This video shows the simulation of a 1D square well using the Periodic Potential Lab. The calculated output includes plots of the allowed energybands, a table of the band edges and band gaps, plots of reduced and expanded dispersion relations, and plots comparing the dispersion relations to...
Quantum Ballistic Transport in Semiconductor Heterostructures
27 Aug 2007 | | Contributor(s):: Michael McLennan
The development of epitaxial growth techniques has sparked a growing interest in an entirely quantum mechanical description of carrier transport. Fabrication methods, such as molecular beam epitaxy (MBE), allow for growth of ultra-thin layers of differing material compositions. Structures can be...
Quantum Dot Lab
12 Nov 2005 | | Contributor(s):: Prasad Sarangapani, James Fonseca, Daniel F Mejia, James Charles, Woody Gilbertson, Tarek Ahmed Ameen, Hesameddin Ilatikhameneh, Andrew Roché, Lars Bjaalie, Sebastian Steiger, David Ebert, Matteo Mannino, Hong-Hyun Park, Tillmann Christoph Kubis, Michael Povolotskyi, Michael McLennan, Gerhard Klimeck
Compute the eigenstates of a particle in a box of various shapes including domes, pyramids and multilayer structures.
Quantum Dot Lab Demonstration: Pyramidal Qdots
This video shows the simulation and analysis of a pyramid-shaped quantum dot using Quantum Dot Lab. Several powerful analytic features of this tool are demonstrated.
Quantum Dot Lab Learning Module: An Introduction
02 Jul 2007 | | Contributor(s):: James K Fodor, Jing Guo
THIS MATERIAL CORRESPONDS TO AN OLDER VERSION OF QUANTUM DOT LAB THAN CURRENTLY AVAILABLE ON nanoHUB.org.
The Diatomic Molecule
31 Mar 2009 | | Contributor(s):: Vladimir I. Gavrilenko