<p> DelColRow(,,) </p>

cd113b67-07a0-4b31-aed4-8f0b619a7c72 24 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

M c DelColRow N 0 : ct 1 : n 1 M cols range n c ≠ N 1 ct el M n col : ct ct 1 + : 21 line if for Unest v N 1 el : j 2 N cols range v v N j el augment : for v 71 line :

Two-dimensional Fourier momentum

Fourier Quantum

Adapted from Mathcad 11, mathengjmg [web site].

Written permission from Frank Rioux.

http://www.users.csbsju.edu/~frioux/workinprogress.html

=> Most interesting for Mathcad users <=

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N 100 ≡ mask 6 min * ≡ Fourier 28 min * ≡ 31 mat

A 30 : a A 2 / : 12 mat R 1.5 : (outer ring ≡ r 1 : (inner ring ≡ d 0.125 : (holes dimension ≡ N 50 : (canvas size => even ≡ 51 line

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

'R' hole positions m 1 A 2 / range θ 1 el 0 : x 1 el 0 : y 1 el 0 : θ m 1 + el 2 π * m * a / : x m 1 + el R θ m 1 + el sin * : y m 1 + el R θ m 1 + el cos * : 61 line for

'r' hole positions m 16 A range θ 16 el 2 π * 6 * a / : x 16 el 0 : y 16 el y 16 el : θ m 1 + el 2 π * m * a / : x m 1 + el r θ m 1 + el sin * : y m 1 + el r θ m 1 + el cos * : 61 line for

coordinate-space wave fnct Δ 30 : j 1 N range px 1 el Δ - : py 1 el Δ - : px j 1 + el Δ - 2 Δ * j * N / + : py j 1 + el Δ - 2 Δ * j * N / + : 41 line for 21 line

Fourier integral transform from wave function into momentum px py Φ 12 π * d * A sqrt * / i px * x * - exp x x m el d 2 / - x m el d 2 / + int i py * y * - exp y y m el d 2 / - y m el d 2 / + int * (m 1 A sum 11 line * ≡

i b * px * - exp - 15 i * px * - exp + (i d * py * - exp i c * py * - exp - (* px py * / a x m el d 2 / - (≡ b x m el d 2 / + (≡ c y m el d 2 / - (≡ d y m el d 2 / + (≡ 14 mat 21 line

Optimiz => SYMBOLIC ... a bit faster px py Ψ 12 π * d * A sqrt * / i x m el d 2 / + (* px * - exp i x m el d 2 / - (* px * - exp - (i y m el d 2 / + (* py * - exp - i y m el d 2 / - (* py * - exp + (* px py * 1012 -^+ / m 1 A sum 11 line * :

t0 1 time :

Optimiz => Numeric P m 1 N range n 1 N range Fo m n el px m el py n el Ψ abs (2^eval : for for Fo 21 line :

P P : C P 0255 Scale : C C N 2 / 1 + DelColRow : C C transpose N 2 / 1 + DelColRow transpose : 41 line

x f 11 x 0.125^+ / : fmap C f vectorize : fmap fmap - 0255 Scale : 31 line

1 time t0 - min 7.6

image C:\SmathFile\FourierQuantum 2C.png READBMP :

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fmap

α 3 : (highlight image ≡

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 α image *

set N=100, export 'C' in your SmathFile, read back 'image' in blank work sheet, experiment 'α'

Mask pattern Two-dimensional concentric circles

t0 1 time :

A 30 : a A 2 / : 12 mat R 1.5 : (outer ring ≡ r 1 : (inner ring ≡ d 0.125 : (holes dimension ≡ size 50 : (canvas size => even ≡ 51 line

outer holes position i 0 a range : x R 2 π * i * 15 / sin * vectorize : y R 2 π * i * 15 / cos * vectorize : y 1 el 0 : 41 line

inner holes position j 16 A range : vx r 2 π * j * 15 / sin * vectorize : vy r 2 π * j * 15 / cos * vectorize : 31 line

Coordinates 
space wave function k 0 size range : xx 2 R * - 4 R * k * size / + vectorize : yy 2 R * - 4 R * k * size / + vectorize : 31 line

Position wave
function Δ 30 : N 30 : i 0 N range : px Δ - 2 Δ * i * N / + vectorize : py px : 51 line

x x vx stack : y y vy stack : 21 line

The 'mask' pattern of the space wave function xx yy Ψ 1 A sqrt / 1 d / xx x m 1 + el d 2 / - (≥ (xx x m 1 + el d 2 / + ≤ (* yy y m 1 + el d 2 / - (≥ (* yy y m 1 + el d 2 / + ≤ (* 0 cases m 1 A sum 11 line * :

Display mask i 1 size range j 1 size range M i j el xx i el yy j el Ψ abs (2^eval : for for

M M 0255 Scale :

iVBORw0KGgoAAAANSUhEUgAAADIAAAAyCAIAAACRXR/mAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAB1SURBVFhH7dI5DoAwDETR3P/QFggoLNygBLzg/6qk8mScAQAAWhCR63S4Xf2EDf65yF71bO8cdl7JHxZf2xMlq52x8lCnktrsIoRudz83KzvRc1eiNNuaNVdAltqcctgx2f+Nzpc966lGym+V3BSLAwDgBWNs0MRcR6zoExQAAAAASUVORK5CYII=

Mask pattern

1 time t0 - min 1.3