Search results
Results From The WOW.Com Content Network
The simplest 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 with impenetrable barriers at either end. [1] The walls of a one-dimensional box may be seen as regions of space with an infinitely large potential energy.
In some cases, the Schrödinger equation can be solved analytically on a one-dimensional lattice of finite length [6] [7] using the theory of periodic differential equations. [8] The length of the lattice is assumed to be L = N a {\displaystyle L=Na} , where a {\displaystyle a} is the potential period and the number of periods N {\displaystyle ...
The wave function of the ground state of a particle in a one-dimensional box is a half-period sine wave, which goes to zero at the two edges of the well. The energy of the particle is given by h 2 n 2 8 m L 2 {\textstyle {\frac {h^{2}n^{2}}{8mL^{2}}}} , where h is the Planck constant , m is the mass of the particle, n is the energy state ( n ...
The one-dimensional infinite square well of length L is a model for a one-dimensional box with the potential energy: = {, < < +,,. It is a standard model-system in quantum mechanics for which the solution for a single particle is well known.
AndyTheGrump: I think our Particle in a box page may help clarify. The use of a conceptual/mathematical solution in one dimension makes the math more tractable, with solutions generalizable to higher dimensions. -- Scray 17:14, 7 October 2012 (UTC) It's analogous to the 3D problem.
The potential may be external or it may be the result of the presence of another particle; in the latter case, one can equivalently define a bound state as a state representing two or more particles whose interaction energy exceeds the total energy of each separate particle. One consequence is that, given a potential vanishing at infinity ...
The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy inside a certain region and infinite potential energy outside .
The size of the simulation box must also be large enough to prevent periodic artifacts from occurring due to the unphysical topology of the simulation. In a box that is too small, a macromolecule may interact with its own image in a neighboring box, which is functionally equivalent to a molecule's "head" interacting with its own "tail".