File:Particle in a box wavefunctions.svg

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Particle_in_a_box_wavefunctions.svg‎ (SVG file, nominally 699 × 600 pixels, file size: 14 KB)

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Summary[edit]

Description
English: Wavefunctions and energies for particle trapped in an infinitely deep quantum well of width L. The spatial position is shown along the horizontal axis, and the energy along the vertical axis. The grey regions represent barriers with an infinitely large potential, while the white area represents a well with zero potential.

The particle may only exist in certain discrete states with energy given by

\varepsilon_n = \frac{\hbar^2\pi^2n^2}{2mL^2}

where n is a positive, whole number. The energy of the particle is shown in the figure as a set of horizontal dotted lines, labeled with the corresponding state number.

The wavefunction for each state is given by

\psi(x) = \begin{cases} \sqrt{\frac{2}{L}} \sin\left(\frac{n \pi x}{L}\right); & 0 < x < L \\ 0; & \text{otherwise} \end{cases}
The wavefunctions are shown superimposed on the diagram at the corresponding energies.
Date
Source Own work by uploader. Created using inkscape function plotter extension
Author Papa November
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GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

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File history

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Date/TimeThumbnailDimensionsUserComment
current13:17, 3 September 2009Thumbnail for version as of 13:17, 3 September 2009699×600 (14 KB)Papa November (Increased nominal resolution to improve wiki thumbnail rendering)

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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
<svg-width> 699
<svg-height> 600
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