#!/usr/bin/env python
"""

Plotter forskjellene mellom bosoner og fermioner for H_2 system.


@author Are Raklev
"""

from numpy import *
from matplotlib.pyplot import *
from numpy.polynomial.hermite_e import hermeval


# Definerer losninger av TUSL for H-atom
def psi_100( x ):
    a = 0.0529 # Bohrradius [nm]
    r = abs(x)
    return 1./sqrt(pi*a**3)*exp(-r/a)
def psi_200( x ):
    a = 0.0529 # Bohrradius [nm]
    r = abs(x)
    return sqrt(1./a**3/2.**2)*exp(-r/2./a)*(4.-2.*2.*r/2./a)*sqrt(1./4./pi)

# Lager x-verdier
x = linspace( -0.5, 0.5, 1e3 )

# Offset fra x = 0 for de to elektronene. Tilsvarer sentrum av H-atomene.
x_1 = -0.05
x_2 = 0.05

# Plotter de to elektrontilstandene for seg selv
figure()
plot( x, abs(psi_100(x+x_1))**2, label='$|\psi_{100}(x_1,0,0)|^2$')
plot( x, abs(psi_200(x+x_2))**2, label='$|\psi_{200}(x_2,0,0)|^2$')

# Tekst langs x-aksen
xlabel('$x$ [nm]')

# Tekst langs y-aksen
ylabel('$|\psi (x,0,0)|^2$ [nm$^{-3}$]')

#
legend(loc='best')

# Plotter de forskjellige topartikkeltilstandene
figure()
# Adskillbare partikler
#plot( x, abs(psi_100( x+x_1 )*psi_200( x+x_2 ))**2, label='$|\psi_{100}(x_1,0,0)\psi_{200}(x_2,0,0)|^2$')
# Bosoner
plot( x, 0.5*abs(psi_100(x+x_1)*psi_200(x+x_2) + psi_200(x+x_1)*psi_100(x+x_2))**2, label='$|\psi_{100}(x_1,0,0)\psi_{200}(x_2,0,0)+\psi_{200}(x_1,0,0)\psi_{100}(x_2,0,0)|^2$')
# Fermioner
plot( x, 0.5*abs(psi_100(x+x_1)*psi_200(x+x_2) - psi_200(x+x_1)*psi_100(x+x_2))**2, label='$|\psi_{100}(x_1,0,0)\psi_{200}(x_2,0,0)-\psi_{200}(x_1,0,0)\psi_{100}(x_2,0,0)|^2$')

# Setter tittel
title('$H_2$')

# Tekst langs x-aksen
xlabel('$x$ [nm]')

# Tekst langs y-aksen
ylabel('$|\psi (x,0,0)|^2$ [nm$^{-3}$]')

#
legend(loc='best')

# Lagre som .eps fil
savefig('H2.eps')


# Viser plottet
show()