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{ 1D_FINITE_POTENTIAL_WELL.PDE
Submitted by Ali Reza Ghaffari, 07/22/2016.
This script solves the Schrodinger equation for a one dimensional finite potential well
and finds energy levels for bound states plus unnormalaized wave functions.
}
TITLE '1D Finite Potential Well'
COORDINATES CARTESIAN1
VARIABLES Phi
SELECT
modes=3
NGRID=30
ERRLIM=1e-3
DEFINITIONS
volt { in eV}
hbar=1.05457e-34
e0=1.6022e-19
m0=9.11e-31
v0=64
a=1.8e-10
EQUATIONS
Phi: (-hbar^2/2/m0/e0)*(dx(dx(Phi)))+volt*Phi-LAMBDA*Phi=0
BOUNDARIES
REGION 1
volt=v0
START (-3*a) point value(phi)=0
LINE TO (-a/2)
REGION 2
volt=0
START (-a/2) LINE TO (a/2)
REGION 3
volt=v0
START (a/2)
LINE TO (3*a ) point value(phi)=0
!MONITORS
! no monitors since problem solves so fast
PLOTS
elevation(phi*5+lambda,volt) from (-3e-10) to (3e-10)
SUMMARY
REPORT(LAMBDA)
END