def femharmosc(n=128,hL=6.0,k=1.0):
doplot = False
# hL stands for half-L, since I want the potential to go between +/- L/2
L = 2*hL
dx = L/float(n)
X = [-hL+dx*i for i in range(1,n)]
T = Tfem(n,L)
S = Sfem(n,L)
V = zeros((n-1,n-1),'d')
for i in range(n-1):
xi = X[i]
V[i,i] = 0.5*k*(dx**3/15. + 2*dx*xi**2/3.)
if i < n-2:
V[i,i+1] = V[i+1,i] = 0.5*k*(dx**3/20. + dx**2*xi/6. + dx*xi**2/6.)
eval,evec = geigh(T+V,S)
print eval[:6]
if doplot:
Xx,Ex,Vx = Exact(100,hL)
print eval[:min(5,n)]
phase0 = sign(evec[5,0])/sign(Vx[5,0])
plot(X,phase0*evec[:,0],'bo',label="0 FEM/32")
plot(Xx,Vx[:,0],'b-',label="0 Exact")
phase1 = sign(evec[5,1])/sign(Vx[5,1])
plot(X,phase1*evec[:,1],'go',label="1 FEM/32")
plot(Xx,Vx[:,1],'g-',label="1 Exact")
title("Harmonic oscillator wave functions")
xlabel("x")
legend()
savefig("/Users/rmuller/Documents/tex/fem-pbox/fem-harmosc.eps")
show()
return
def main(n=10,**kwargs):
xmax = kwargs.get('xmax',2.0)
xmin = kwargs.get('xmin',-xmax)
small = kwargs.get('small',1e-10)
L = xmax-xmin
dx = L/float(n)
Xdvr,Edvr,Udvr = dvr(xmax=xmax,xmin=xmin)
X = [xmin+i*dx for i in range(1,n)]
T = Tfem(n,L)
S = Sfem(n,L)
V = zeros((n-1,n-1),'d')
for i in range(n-1):
xi = X[i]
ax = abs(xi)
V[i,i] = 1
# Commented out since it wouldn't compile:
# if xi > dx:
# V[i,i] =
# if abs(xi) > tol:
# V[i,i] += 4*
# V[i,i] = -2*ax/dx \
# + pow((dx-ax)/dx,2)*(loga(xi)-loga(xi-dx)) \
# + pow((dx+ax)/dx,2)*(loga(xi+dx)-loga(xi))
#if i < n-2:
# V[i,i+1] = V[i+1,i] = (2*ax+dx)/(2*dx) + ax*(dx+ax)/(dx*dx) *\
# (loga(xi+dx)-loga(xi))
E,U = geigh(T+V,S)
print E[:4]
print Edvr[:4]
print X
plot(Xdvr,abs(Udvr[:,0]),'b-')
plot(X,abs(U[:,0]),'bo')
show()
def main(n=30,**kwargs):
L = kwargs.get('L',5.0)
Z = kwargs.get('Z',1.0)
tol = kwargs.get('tol',1e-5)
dx = L/float(n)
X = [i*dx for i in range(1,n)]
T = Tfem(n,L)
S = Sfem(n,L)
V = zeros((n-1,n-1),'d')
for i in range(n-1):
xi = X[i]
V[i,i] = Z + Z*pow((xi+dx)/dx,2)*log(xi+dx)
if abs(xi) > tol:
V[i,i] += 4*Z*xi*log(xi)/dx
if abs(xi-dx) > tol:
V[i,i] += Z*pow((xi-dx)/dx,2)*log(xi-dx)
E,U = geigh(T+V,S)
plot(X,U[:,0])
# Exact solutions, for comparison
E10,Psi10 = ExactH(1,0)
plot(X,[Psi10(x) for x in X],'b-')
print E[0],E10
# DVR solutions, for comparison
#E10dvr,Psi10dvr = DVR(X,1,0)
#plot(X,Psi10dvr,'bo')
show()
