#############################################################################################
# A gnuplot script to plot the finite well potential and the first few
# states of the finite quantum well for V0 = 0.5 Hartrees and L0 = 40 Bohr.
#
#          written by Thomas L. Gibson  November 09, 2011
#############################################################################################
######Normalization Constants
c1 = 0.21820330
c2 = 0.21815880
c3 = 0.21808216
c4 = 0.21796927
######Wave Numbers
k1 = 0.07479650
k2 = 0.14957282
k3 = 0.22430781
k4 = 0.29897818
######Exponential Damping Coefficients
kappa1 = 0.99719882
kappa2 = 0.98875071
kappa3 = 0.97451834
kappa4 = 0.95425995
######Well Height and Width
V0 = 0.5
L0 = 40
############################################################################################
f(x) = (abs(x) >= 0.5*L0) ? V0 : 0
Y1L(x) = (x <= -0.5*L0) ? c1 * cos(k1*0.5*L0)*exp(0.5*kappa1*L0)*exp(kappa1*x): 1/0
Y1C(x) = (abs(x) <= 0.5*L0) ? c1*cos(k1*x) : 1/0
Y1R(x) = (x >= 0.5*L0) ? c1 * cos(k1*0.5*L0)*exp(0.5*kappa1*L0)*exp(-kappa1*x): 1/0
Y2L(x) = (x <= -0.5*L0) ? -c2 * sin(k2*0.5*L0)*exp(0.5*kappa2*L0)*exp(kappa2*x): 1/0
Y2C(x) = (abs(x) <= 0.5*L0) ? c2*sin(k2*x) : 1/0
Y2R(x) = (x >= 0.5*L0) ? c2 * sin(k2*0.5*L0)*exp(0.5*kappa2*L0)*exp(-kappa2*x): 1/0
Y3L(x) = (x <= -0.5*L0) ? c3 * cos(k3*0.5*L0)*exp(0.5*kappa3*L0)*exp(kappa3*x): 1/0
Y3C(x) = (abs(x) <= 0.5*L0) ? c3*cos(k3*x) : 1/0
Y3R(x) = (x >= 0.5*L0) ? c1 * cos(k3*0.5*L0)*exp(0.5*kappa3*L0)*exp(-kappa3*x): 1/0
Y4L(x) = (x <= -0.5*L0) ? -c4 * sin(k4*0.5*L0)*exp(0.5*kappa4*L0)*exp(kappa4*x): 1/0
Y4C(x) = (abs(x) <= 0.5*L0) ? c4*sin(k4*x) : 1/0
Y4R(x) = (x >= 0.5*L0) ? c4 * sin(k4*0.5*L0)*exp(0.5*kappa4*L0)*exp(-kappa4*x): 1/0
#set nokey
set key top center
set title "Finite Well: V0 = 0.5 Hartrees; L0 = 40 Bohr"
plot [-L0: L0] [-0.25: V0 + 0.25] f(x) t 'V(x)' lw 3 lc rgb 'black',\
     Y1L(x) t 'Y1' lw 2 lt 1 lc rgb 'red',\
     Y1C(x) t ''lw 2 lt 1 lc rgb 'red',\
     Y1R(x) t ''lw 2 lt 1 lc rgb 'red',\
     Y2L(x) t 'Y2' lw 2 lt 3 lc rgb 'blue',\
     Y2C(x) t '' lw 2 lt 3 lc rgb 'blue',\
     Y2R(x) t '' lw 2 lt 3 lc rgb 'blue',\
     Y3L(x) t 'Y3' lw 2 lt 5 lc rgb 'green',\
     Y3C(x) t '' lw 2 lt 5 lc rgb 'green',\
     Y3R(x) t '' lw 2 lt 5 lc rgb 'green',\
     Y4L(x) t 'Y4' lw 2 lt 7 lc rgb 'orange',\
     Y4C(x) t '' lw 2 lt 7 lc rgb 'orange',\
     Y4R(x) t '' lw 2 lt 7 lc rgb 'orange'
set xlabel "x (Bohr)"
pause -1 "Hit return to make finite_well.ps or cntl c to exit."
#z(x) = 0
set terminal postscript enhanced
set output "finite_well.ps"
#set nokey
set key top center
set title "Finite Well: V_{0} = 0.5 Hartrees; L_{0} = 40 Bohr"
plot [-L0: L0] [-0.25: V0 + 0.25] f(x) t 'V(x)' lw 3 lc rgb 'black',\
     Y1L(x) t '{/Symbol y}_{1}' lw 2 lt 1 lc rgb 'red',\
     Y1C(x) t ''lw 2 lt 1 lc rgb 'red',\
     Y1R(x) t ''lw 2 lt 1 lc rgb 'red',\
     Y2L(x) t '{/Symbol y}_{2}' lw 2 lt 3 lc rgb 'blue',\
     Y2C(x) t '' lw 2 lt 3 lc rgb 'blue',\
     Y2R(x) t '' lw 2 lt 3 lc rgb 'blue',\
     Y3L(x) t '{/Symbol y}_{3}' lw 2 lt 5 lc rgb 'green',\
     Y3C(x) t '' lw 2 lt 5 lc rgb 'green',\
     Y3R(x) t '' lw 2 lt 5 lc rgb 'green',\
     Y4L(x) t '{/Symbol y}_{4}' lw 2 lt 7 lc rgb 'orange',\
     Y4C(x) t '' lw 2 lt 7 lc rgb 'orange',\
     Y4R(x) t '' lw 2 lt 7 lc rgb 'orange'
set xlabel "x (Bohr)"
reset
exit