One-Slit Diffraction Pattern

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The time-dependent Schrödinger equation is solved for a slit of width , bounded by rigid walls in the region , . Various representations of the real part, imaginary part, and absolute values of the diffraction pattern are shown for time .

Contributed by: Enrique Zeleny (November 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The equations are

,

,

with initial conditions

,

,

and boundary conditions (the slit is gradually opened to be consistent)

,

,

,

,

,

,

,

,

where and are equal to 10,

,

is a parameter with an integer value, and is the time needed to fully open the slit;

,

where is the de Broglie wavelength. We set .

References

[1] D. A. Garanin, "Partial Differential Equations." (Nov 13, 2014) www.lehman.edu/faculty/dgaranin/Mathematical_Physics/Mathematical_physics-13-Partial_differential _equations.pdf.

[2] M. Beau and T. C. Dorlas, "Three-Dimensional Quantum Slit Diffraction and Diffraction in Time." arxiv:1310.5614v3.



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