def solve4l(l):
def CombinedPotential(r):
return LennardJonesPotential(e, s, r) + l*(l+1)/(mh*r**2)
# initialize the (combined) potential
self._V = array(map(lambda r: CombinedPotential(r), self._r))
# initialize the k's, based on the potential
self._k = mh*(E-self._V)
for i in xrange(r0_pos, len(self._r)-1):
self._u[i+1] = numerov(self._dr, self._k[i], self._u[i], self._k[i-1], self._u[i-1], self._k[i+1])
from numerov import numerov
# Specific function k used in the schrödinger equation
k = lambda z, eps: eps - z
# The values for eps
eps = np.array([5.0, 6.0])
# Number of steps N and step size dz
N = 10000
dz = 0.001
# Initial valuess
z0 = 0.0
psi0 = 0.0
psid0 = 1.0
# Plot the solutions of the numerov algorithm and save them
plt.axis([0, 10, -1, 1])
for e in eps:
k_eps = lambda x: k(x, e)
z, psi = numerov(z0, psi0, psid0, k_eps, dz, N)
plt.plot(z, psi)
plt.xlabel(r'$\eta$')
plt.ylabel(r'$\psi(\eta)$')
if not os.path.exists('figures'):
os.mkdir('figures')
plt.savefig('figures/fig2_1.pgf')
plt.show()
#!/usr/bin/python
from numerov import numerov
import numpy as np
def VBound(c):
return lambda x : 0 <= x <= 1 and c * (x**2 - x) or 0
def k_gen(V):
return lambda x : 2 * (E - V(x))
if __name__ == '__main__':
dx = 0.001
c = 1e3
integrator = numerov(dx)
V = VBound(c)
k = k_gen(V)
# choose a point b
b = 0.5
E = V(b)*1e2
psiL0 = np.exp(-1j * np.sqrt(np.complex(k(0))) * -dx)
psiR0 = np.exp(-1j * np.sqrt(np.complex(k(1))) * (1+dx))
psiL1 = psiR1 = 1
pli = [psiL0, psiL1]
pri = [psiR0, psiR1]
psiL = integrator.integrate(0, b, k, pli)
integrator.dx = -dx
def epsSlider_onChanged(eps):
k_eps = lambda x: eps - x
z, psi = numerov(z0, psi0, psid0, k_eps, dz, N)
lines.set_data(z, psi)
def psi_limit(eps): """ Returns the last value of the solution psi """ k_eps = lambda z: k(z, eps) psi = numerov(z0, psi0, psid0, k_eps, dz, N)[1] return psi[N - 1]
