def take_step(self):
# first half of potential phase rotation
for j in range(self.N):
self.psi[j] *= self.V_exp_factor[j]
# FFT to momentum space
self.psi = cpt.fft(self.psi)
# kinetic phase rotation
for j in range(self.N):
self.psi[j] *= self.T_exp_factor[j]
# FFT back to position space
do_inverse = True
self.psi = cpt.fft(self.psi, do_inverse)
# second half of potential phase rotation
for j in range(self.N):
self.psi[j] *= self.V_exp_factor[j]
self.t += self.dt
def take_step(self):
# first half of potential phase rotation
for j in range(self.N):
self.psi[j] *= self.V_exp_factor[j]
# FFT to momentum space
self.psi = cpt.fft(self.psi)
# kinetic phase rotation
for j in range(self.N):
self.psi[j] *= self.T_exp_factor[j]
# FFT back to position space
do_inverse = True
self.psi = cpt.fft(self.psi, do_inverse)
# second half of potential phase rotation
for j in range(self.N):
self.psi[j] *= self.V_exp_factor[j]
self.t += self.dt
q = 10.0 # point charge
jq = kq = int(N / 2) # at center of lattice
rho = cpt.Matrix(N, N)
for j in range(N):
for k in range(N):
if j == jq and k == kq:
rho[j][k] = q / h**2
else:
rho[j][k] = 0.0
# FFT rows of rho
f = [ 0.0 ] * N # to store rows and columns
for j in range(N):
for k in range(N):
f[k] = rho[j][k]
f = cpt.fft(f)
for k in range(N):
rho[j][k] = f[k]
# FFT columns of rho
for k in range(N):
for j in range(N):
f[j] = rho[j][k]
f = cpt.fft(f)
for j in range(N):
rho[j][k] = f[j]
# Solve equation in Fourier space
V = cpt.Matrix(N, N)
W = cmath.exp(1.0j * 2 * math.pi / N)
Wm = Wn = 1.0 + 0.0j