> For the complete documentation index, see [llms.txt](https://servicio-social.gitbook.io/computational-physics/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://servicio-social.gitbook.io/computational-physics/time-dependent-schrodinger-equation/wave-particle-duality.md).

# Wave-particle duality

<figure><img src="https://2276973797-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FB1IXpWfKDLiUtuVnth7p%2Fuploads%2F9ndyRYf2qFlsPlhSTGww%2FDiffraction.gif?alt=media&amp;token=841a0dbf-4625-4587-92e9-053f97b2e02c" alt=""><figcaption></figcaption></figure>

<figure><img src="https://2276973797-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FB1IXpWfKDLiUtuVnth7p%2Fuploads%2Fjngd1M78dbWVy6ZBxAJe%2FInterference.gif?alt=media&amp;token=c66fdd92-624f-4059-b017-1ef548803831" alt=""><figcaption></figcaption></figure>

<pre><code>Numerical Domain
<strong>(x,y) in [-1.5,1.5]x[-1.5,1.5]
</strong>Nx = Ny = 300
CFL = 0.125
Nt = 4000

Initial conditions
k0 = 12.5 pi
aX = 0.3
aY = 0.3
psi = (2.0d0/pi/aX/aY)**0.5* exp(-((x+0.8)/X)**2 - (y/aY)**2) &#x26;
      * exp(cmplx(0.0d0,k0*x))
      
Single Slit Potential
if (|x|&#x3C;=0.025  and |y|>0.25) then
    V = 6000
else
    V = 0
end if

Double Slit Potential
if (|x|&#x3C;=0.025  and y in [-1.5,0.375)U(-0.225,0.225)U(0.375,1.5] ) then
    V = 6000
else
    V = 0
end if

</code></pre>

<figure><img src="https://2276973797-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FB1IXpWfKDLiUtuVnth7p%2Fuploads%2FC9lA4PafB5nYmR0LGIpC%2FRefraction.gif?alt=media&amp;token=1c8ba7cb-deae-439a-8bdd-0a27b4a62879" alt=""><figcaption></figcaption></figure>

```
Numerical Domain
(x,y) in [-2,2]x[-2,2]
Nx = Ny = 400
CFL = 0.125
Nt = 5000

Initial conditions
k0 = 15 pi
aX = 0.15
aY = 0.15
psi = (2/pi/aX/aY)**0.5 * exp(-((x+0.6)/aX)**2 - ((y+1.2)/aY)**2)
      * exp(cmplx(0,k0*(cos(34*pi/180)*x+y*sin(34*pi/180))))
      
Potential
if (x <= 0) then
    V = 0
else
    V = 750
end if

```

<figure><img src="https://2276973797-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FB1IXpWfKDLiUtuVnth7p%2Fuploads%2F75Rl5Su3inSmbG6epfH7%2FDispersionCentral.gif?alt=media&amp;token=a4b3b040-a7dc-4f3b-b49f-5e434d8085e2" alt=""><figcaption></figcaption></figure>

```
Numerical Domain
(x,y) in [-1.5,1.5]x[-1.5,1.5]
Nx = Ny = 300
CFL = 0.125
Nt = 6000

Initial conditions
k0 = 10 pi
aX = 0.15
aY = 0.15
psi = (2/pi/aX/aY)**0.5* exp(-((x+0.7)/aX)**2 - (y/aY)**2) 
    * exp(cmplx(0.0d0,k0*x))
      
Potential
V = 500 * exp(-0.5*(x**2+y**2)/(0.3)**2)

```