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.
The finite potential well (also known as the finite square well) is a concept from quantum mechanics.It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls".
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.
For the case of one particle in one spatial dimension, the definition is: ^ = where ħ is the reduced Planck constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by /) is used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator.
between the position operator x and momentum operator p x in the x direction of a point particle in one dimension, where [x, p x] = x p x − p x x is the commutator of x and p x , i is the imaginary unit, and ℏ is the reduced Planck constant h/2π, and is the unit operator.
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.
The energy levels of a single particle in a quantum dot can be predicted using the particle in a box model in which the energies of states depend on the length of the box. For an exciton inside a quantum dot, there is also the Coulomb interaction between the negatively charged electron and the positively charged hole.
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 ...