def Bmat(N, k, rmin, rmax):
dim = N - k - 2
t = knotSeq(k, N, rmin, rmax)
BB = zeros((dim, dim))
for ii in range(0, dim):
for jj in range(0, dim):
i = ii + 2
j = jj + 2
if abs(i - j) <= k - 1:
BB[ii][jj] = B_GQint(k, t, i, j)
else:
BB[ii][jj] = 0.0
return BB
def Hmat(N, k, rmin, rmax, l, Z):
dim = N - k - 2
print("Hmat dim: %i " % dim)
t = knotSeq(k, N, rmin, rmax)
H = zeros((dim, dim))
t1f = 0.5 #hbar**2/(2*m_e)
t2f = 0.5 * (l * (l + 1)) #hbar^2*l(l+1)/2m_e
t3f = -1 * Z #-Z*e^2/(4*pi*epsilon_0)
for ii in range(0, dim):
for jj in range(0, dim):
i = ii + 2
j = jj + 2
if abs(i - j) <= k - 1:
term1 = t1f * H_GQint(k, t, i, j, term=1)
term2 = t2f * H_GQint(k, t, i, j, term=2)
term3 = t3f * H_GQint(k, t, i, j, term=3)
H[ii][jj] = term1 + term2 + term3
else:
H[ii][jj] = 0.0
return H
plt.rcParams.update(params)
plt.rc('lines', linewidth=2)
plt.rc('axes',
prop_cycle=(cycler('color', ['c', 'r', 'm', 'y', 'b']) +
cycler('linestyle', ['-', '-', '-', '-', '-'])))
HtGS = (13.6 / 27.211385) # ~= 0.5 Hartree
Hh = Hmat(N, k, rmin, rmax, l, Z)
Bb = Bmat(N, k, rmin, rmax)
#print Hh[-1][-1], Bb[-1][-1] #SEEMS TO WORK
w, vr = LA.eig(Hh, Bb)
tt = knotSeq(k, N, rmin, rmax)
xx = linspace(rmin, rmax, 1000)
minidx = argwhere(w < 0)
minidx = minidx[:, 0]
#print minidx, len(minidx)
#print w
aPsi2n1 = pow(abs(xx * aPsi(xx, 1, l)), 2)
aPsi2n1 = aPsi2n1 / sum(aPsi2n1)
aPsi2n2 = pow(abs(xx * aPsi(xx, 2, l)), 2)
aPsi2n2 = aPsi2n2 / sum(aPsi2n2)
aPsi2n3 = pow(abs(xx * aPsi(xx, 3, l)), 2)
aPsi2n3 = aPsi2n3 / sum(aPsi2n3)
apsilab = r'Analytic $r^2 |R_{n,l}(r)|^2$'
if Z == 1 and lcompflag == 0:
