8c8cb406-7172-4e5f-98c4-bcad2d1d80a0 67 4 5 decimal

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

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

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x r Ψ 12 r * sqrt / x r - ≥ (x r ≤ (* 0 cases :

Fourier Quantum: pin hole diffraction

x f x 2 Ψ abs (2^:

x g 0 :

coordinate-space prob. density

f g 2 - 2 10 hatch 2 1 sys

"Diffraction has a simple quantum mechanical interpretation based on the uncertainty principle. Or, one could say: diffraction is an excellent way to illustrate the uncertainty principle. A screen with a single hole of radius 'r' is illuminated with a coherent photon of particle beam. The normalized coordinate-space wave function @ the slit screen .......... Ψ(x,r) Since the hole-screen measures position, it localizes the incident beam in the X-direction. According to the uncer- tainty principle, because position and momentum are incom- patible, or conjugate, observables, this measurement must be acompanied by a delocalization of the X-component of the momentum. To see this, it necessary to Fourier transform Y(x,w) into momentum space to obtain the momentum wave function Φ(px,r) ...

W 0.5 : M 0.0375 : xo 0 : 13 mat U 10000 : α 4 : 12 mat 21 line

px r Φ 12 π * sqrt / i px * x * - exp x r Ψ * x r - r int * ≡

x q 0.1 12 x xo - (* U * W / (α^+ (M^/ :

... it is the momentum distribution, (|Φ(px,r)|)², shown belowthat is projected onto the detection screen. Thus, a position measurement @ the detection screen is also effectively a measure of the X-component of the partile momentum." Frank Rioux with permission Mathcad 11.

The mapping function

x q

r 0.5 : (pin hole radius ≡ Δ 30 : N 30 : (canvas size ≡ 31 line

convenient
demo setup r 0.25 ≡ Δ 48 ≡ N 49 ≡ 31 line

position wave fnct
@ hole screen j 0 N range : x 1 - 2 j * N / + vectorize : y 1 - 2 j * N / + vectorize : 31 line

bidirectional
position momentum j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 31 line

asymmetric mapping x f 11 x 0.325^+ / :

x f

position wave function @ hole screen x y Ψ 1 x r - ≥ (x r ≤ (* y r 2^x 2^- sqrt Re - ≥ (* y r 2^x 2^- sqrt Re ≤ (* 0 cases :

coordinate-space wave function D i 1 N range j 1 N range hole i j el x i el y j el Ψ (2^eval : for for hole 21 line :

D D 0255 Scale :

iVBORw0KGgoAAAANSUhEUgAAAB4AAAAeCAIAAAC0Ujn1AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABhSURBVEhL7cyxCsAgEERB//+jQ5pJEVBctQnkpjz2XSvlx64310Oe9Vjs8WPMbpV6xnqJdMY6p8toQqKMJiTKaEKijCYkymhyuhnrJdIZ61XqMbs9fvRYHPLs4VrKF7V2Ax/9Dvmap9xXAAAAAElFTkSuQmCC D

The double integrator needs [x ,y] be scalar => 'Clear' must be evaluated as shown.

x y Clear 1

The reduced symbolic double integrand i px * x * - exp i py * y * - exp * i px x * y py * + (* - exp ≡

Optimiz numeric, set options integral accuravy 50 px py Φ i px x * y py * + (* - exp y r 2^x 2^- vectorize sqrt - r 2^x 2^- vectorize sqrt int x r - r int :

Δ N 12 mat 20 ≡ (70 min * ≡ Δ N 12 mat 30 ≡ (159 min * ≡ 21 mat

t0 1 time :

P m 1 N range n 1 N range Fo m n el px m el py n el Φ vectorize abs (2^: for for Fo 21 line :

P P : x f x q : fmap P f vectorize : CoC fmap - 0255 Scale : 41 line

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 CoC

1 time t0 - min 158.8

chr char ≡

sz size ≡

clr color ≡

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr augment stack : for plot 41 line :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct eval : for U f augment 31 line :

{Δ, N] ... min Data 3 1.6 5 4.3 7 8.4 10 16.9 207030 158.8 62 mat :

X Data 1 col : Y Data 2 col : 21 line

x φ 1 x x 2^31 mat :

j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 0.1393 0.0869 - 0.1774 31 mat

x fit b x φ * :

Setup the plot

hr 1 :

Poly 0 - 501 x fit inc :

data X Y . 14 red plotG :

48 fit 60 / hr 6.8

Predict Quantum

Poly data 2 1 sys