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# 2d_finite_potential_well

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# 2d_finite_potential_well

{ 2D_FINITE_POTENTIAL_WELL.PDE

Submitted by Ali Reza Ghaffari, 07/22/2016.

This script solves the Schrodinger equation for a two dimensional finite potential well.

This script finds energies and wave functions of a wire with rectangle cross section.

The wire is made up of GA As which is placed in a AlGalAs medum.

}

TITLE 'infinitely deep rectangular wires'

COORDINATES cartesian2

VARIABLES Phi     {the wavefunction}

SELECT

modes=4

NGRID=13

ERRLIM=1e-3

painted             { show colour-filled contours }

thermal_colors = on { red is minimum }

DEFINITIONS

mass{default value}

volt { in eV}

hbar=1.05457e-34

m0=9.11e-31

e0=1.6e-19

xx=200e-10

yy=200e-10

x1=50e-10

y1=50e-10

x2=150e-10

y2=150e-10

v0=.228

mass_shell=0.067*m0 {mhh}!0.067 {GaAs}

mass_core=0.1*m0!  {Al0.5Ga0.5As}

N=integral(phi^2)

EQUATIONS

BOUNDARIES

Region 1

mass= mass_shell, volt=v0

start(0,0)

point value (phi)=0 line to (xx,0)

value (phi)=0 line to (xx,yy)

value (phi)=0 line to (0,yy)

to close

Region 2

mass= mass_core, volt=0

start(x1,y1)

line to (x2,y1) to (x2,y2) to (x1,y2)

to close

!MONITORS

! no monitors since problem solves so fast

PLOTS

CONTOUR(Phi^2/sqrt(N))

SUMMARY

REPORT(LAMBDA*1000) as "Energy Level (meV)" !in milielectron volt

END