One-Slit Diffraction Pattern

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 .

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