def run(Ns, step, dt, acc, c):
args = (m, omega, acc, x0, c)
v = harmonic_potential(x, t, args=args)
sch = Schrodinger(x, psi_x, v, k, hbar=hbar, m=m, t=0, args=args)
for i in range(Ns):
sch.evolve_t(N_steps=step, dt=dt)
return sch.expectation_x()
def run(A, choen=False):
V_x = barrier(x, A, x1, x2)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m, args=x2, t=0)
I = sch.impedencePacket()
while sch.t < finalt:
print("Height :{h} Time:{t}".format(h=A, t=sch.t))
sch.evolve_t(step, dt)
T = sch.barrier_transmition()
return T, I
def runAll(self, N_step=1):
psi_comb = np.zeros((self.n, len(self.x)), dtype=complex)
for initial in self.initarray:
x0, v0, a0, g0 = initial
psi_x = self.hellerPacket(x0, v0, a0, g0)
sch = Schrodinger(self.x, psi_x, self.v, hbar=self.hbar, m=self.m)
for i in range(self.n):
if i != 0:
sch.evolve_t(N_step, self.dt)
psi_sol = sch.psi_x
psi_comb[i] += psi_sol / np.sqrt(self.N_packet)
self.psi_comb = psi_comb
return psi_comb
def run_A(A):
Psi_x = gauss_init(x, k0, x0=x0, d=sig)
V_x = gauss_barrier(x, A, x1, omeg)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m, t=0, args=x1)
imp = sch.impedencePacket(tol=10**-11)
time_list = []
Trans_list = []
while sch.t < t_final:
sch.evolve_t(N_steps=step, dt=dt)
time_list.append(sch.t)
Trans_list.append(sch.barrier_transmition())
print("Height {v}, Time {t}".format(v=A / scale, t=sch.t))
return sch.barrier_transmition(), imp
def run(acc):
t = 0
psi_x = gauss_init(x, k_initial, x0=0, d=d)
V_x = gaussbox(x, w, L, x0=xb, A=Amp, a=acc)
sch = Schrodinger(x, psi_x, V_x, k, hbar=hbar, m=m, t=t)
t_list = []
x_list = []
for i in range(Ns):
sch.evolve_t(N_steps=step, dt=dt)
t_list.append(sch.t)
x_list.append(sch.expectation_x())
dat = list(zip(t_list, x_list))
# np.savetxt("GBox_{}.txt".format(a), dat)
return dat
def run(x2, time=False):
V_x = barrier(x, A, x1, x2)
psi_init = gauss_init(x, k_init, x0=x0, d=sig)
sch = Schrodinger(x, psi_init, V_x, k, hbar=hbar, m=m, t=0, args=x2)
dat = []
t_list = []
for i in range(0, Ns):
sch.evolve_t(step, dt)
dat.append(sch.barrier_transmition())
t_list.append(sch.t)
# plt.plot(sch.k, abs(sch.psi_k))
# plt.show()
if time:
return dat, t_list
else:
return dat
def onePacket(self, vkick, init):
nhalf = int(self.n / 2)
psi_arr = np.zeros((self.n, len(self.x)), dtype=complex)
x0, v0, a0, g0 = init
psi_init = self.hellerPacket(x0, v0, a0, g0)
tempsch = Schrodinger(self.x,
psi_init,
self.v,
hbar=self.hbar,
m=self.m)
for i in range(nhalf):
tempsch.evolve_t(1, dt=self.dt)
psi_arr[i] = tempsch.psi_x
tempsch.momentum_kick(self.m * vkick / self.hbar)
for i in range(nhalf):
tempsch.evolve_t(1, dt=self.dt)
psi_arr[i + nhalf] = tempsch.psi_x
return psi_arr
V_x,
step,
dt,
lim1=((0, x_length), (0, max(np.real(psi_x)))),
lim2=((ks[0], ks[N - 1]), (0, 30)))
a.make_fig()
t_list = []
norm_x = []
expec_x = []
expec_xs = []
expec_k = []
for i in range(Ns):
if i != 0:
sch.evolve_t(step, dt)
t_list.append(sch.t)
norm_x.append(sch.norm_x() - 1)
expec_x.append(sch.expectation_x())
expec_xs.append(np.sqrt(sch.expectation_x_square() - expec_x[i]**2))
expec_k.append(sch.expectation_k())
# x_pos_list = [x_pos(j, x0, k_initial, hbar=hbar, m=m) for j in t_list]
# xdiff = [np.abs(expec_x[n] - x_pos_list[n]) for n in range(len(expec_x))]
# popt1, pcov = curve_fit(func, t_list, x_pos_list)
# print("Expected x :", popt1)
#
# popt2, pcov = curve_fit(func, t_list, expec_x)
# print("Calculated x :", popt2)
#
plt.plot(x, V)
plt.show()
sch = Schrodinger(x, psi_init, V, hbar=hbar, m=m, t=0)
# a = Animate(sch, V, 1, dt,lim1=((-xmax, xmax), (0, max(sch.psi_squared))))
# a.make_fig()
simx = []
tl = []
El = []
temp = 0
while temp < Nt:
sch.evolve_t(1, dt=dt)
temp += 1
if (temp % nsave) == 0:
simx.append(sch.expectation_x())
tl.append(temp * dt)
El.append(sch.energy())
actualx = x_pos(np.asarray(tl), x0, omegax, 0)
diff = abs(np.asarray(simx) - actualx)
plt.plot(tl, simx)
plt.plot(tl, actualx, linestyle="--")
plt.show()
plt.plot(tl, diff)
plt.show()
