def kChange(start, stop, step, show=False):
k_range = np.arange(start, stop, step)
E_list = energy2(k_range, hbar, m, sig)
Es_list = []
for i in k_range:
Psi_x = gauss_init(x, i, x0=x0, d=sig)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m, t=0)
Es_list.append(sch.energy())
Diff_list = [Es_list[j] - E_list[j] for j in range(len(k_range))]
plt.figure()
plt.plot(k_range, E_list, label="Theoretical")
plt.plot(k_range, Es_list, label="Simulated", linestyle="--")
plt.title("k0")
plt.legend()
plt.xlabel("k0")
plt.ylabel("Energy")
plt.savefig("k0.png")
if show:
plt.show()
plt.figure()
plt.plot(k_range, Diff_list, label="Diff")
plt.title("k0_Diff")
plt.legend()
plt.xlabel("k0")
plt.ylabel("k0_Difference")
plt.savefig("k0_diff.png")
if show:
plt.show()
def Nchange(nrange, show=False):
E_ = energy2(k0, hbar, m, sig)
Es_list = []
for i in nrange:
N = 2**i
x = np.array([i * dx for i in range(N)])
x = x - max(x) / 2
Psi_x = gauss_init(x, k0, x0=x0, d=sig)
V_x = np.zeros(N)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m)
Es_list.append(sch.energy())
Diff_list = [Es_list[j] - E_ for j in range(len(nrange))]
plt.figure()
plt.plot(nrange, [E_ for i in nrange], label="Theoretical")
plt.plot(nrange, Es_list, label="Simulated", linestyle="--")
plt.title("N")
plt.legend()
plt.xlabel("N")
plt.ylabel("Energy")
plt.savefig("N.png")
if show:
plt.show()
plt.figure()
plt.ylim()
plt.plot(nrange, Diff_list, label="Diff")
plt.title("N_Diff")
plt.legend()
plt.xlabel("N")
plt.ylabel("Energy_Difference")
plt.savefig("N_diff.png")
if show:
plt.show()
Rel_list = [Diff_list[j] / E_ for j in range(len(nrange))]
plt.figure()
plt.plot(nrange, Rel_list, label="Relative Difference")
plt.title("N Relative Difference")
plt.legend()
plt.xlabel("N")
plt.ylabel("Relative_Energy_Difference")
plt.savefig("N_rel.png")
def mChange(start, stop, step, show=False):
m_range = np.arange(start, stop, step)
E_list = energy2(k0, hbar, m_range, sig)
Es_list = []
for i in m_range:
Psi_x = gauss_init(x, k0, x0=x0, d=sig)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=i, t=0)
Es_list.append(sch.energy())
Diff_list = [Es_list[j] - E_list[j] for j in range(len(m_range))]
plt.figure()
plt.plot(m_range, E_list, label="Theoretical")
plt.plot(m_range, Es_list, label="Simulated", linestyle="--")
plt.title("M")
plt.legend()
plt.xlabel("M")
plt.ylabel("Energy")
plt.savefig("M.png")
if show:
plt.show()
plt.figure()
plt.plot(m_range, Diff_list, label="Diff")
plt.title("M_Diff")
plt.legend()
plt.xlabel("M")
plt.ylabel("Energy_Difference")
plt.savefig("M_diff.png")
if show:
plt.show()
Rel_list = [Diff_list[j] / E_list[j] for j in range(len(m_range))]
av = np.mean(Rel_list)
plt.figure()
plt.ylim(av - 0.1, av + 0.1)
plt.plot(m_range, Rel_list, label="Average.{}".format(round(av, 5)))
plt.title("M Relative Difference")
plt.legend()
plt.xlabel("M")
plt.ylabel("Relative_Energy_Difference")
plt.savefig("M_rel.png")
if show:
plt.show()
def sigChange(start, stop, step, show=False):
sig_range = np.arange(start, stop, step)
E_ = energy2(k0, hbar, m, sig_range)
Es_list = []
for i in sig_range:
Psi_x = gauss_init(x, k0, x0=x0, d=i)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m, t=0)
Es_list.append(sch.energy())
Diff_list = [Es_list[j] - E_[j] for j in range(len(sig_range))]
plt.figure()
plt.plot(sig_range, E_, label="Theoretical")
plt.plot(sig_range, Es_list, label="Simulated", linestyle="--")
plt.title("Sigma")
plt.legend()
plt.xlabel("Sigma")
plt.ylabel("Energy")
plt.savefig("Sigma.png")
if show:
plt.show()
plt.figure()
plt.plot(sig_range, Diff_list, label="Diff")
plt.title("Sigma_Diff")
plt.legend()
plt.xlabel("Sigma")
plt.ylabel("Energy_Difference")
plt.savefig("Sigma_diff.png")
if show:
plt.show()
Rel_list = [Diff_list[j] / E_[j] for j in range(len(sig_range))]
plt.figure()
plt.plot(sig_range, Rel_list, label="Relative Difference")
plt.title("Sigma Relative Difference")
plt.legend()
plt.xlabel("Sigma")
plt.ylabel("Relative_Energy_Difference")
plt.savefig("Sig_rel.png")
if show:
plt.show()
k = fftfreq(N, dk)
ks = fftshift(k)
# Defining time steps
t = 0
dt = 0.01
step = 10
Ns = 100
print("Final time", dt * step * Ns)
hbar = 1
m = 1
sch = Schrodinger(x, psi_x, V_x, k, hbar=hbar, m=m)
print("Numerical Energy :", sch.energy())
print("Theoretical Energy", (hbar**2 * k_initial**2) / (2 * m))
print("Difference :", sch.energy() - (hbar**2 * k_initial**2) / (2 * m))
psi_init2 = gauss_init(x, k_initial, x0=x0, d=d)
psis2 = np.real(psi_init2 * np.conj(psi_init2))
# plt.plot(x, sch.mod_square_x(True))
# plt.plot(x, V_x)
# plt.ylim(0, max(np.real(psi_x)))
# plt.show()
a = Animate(sch,
V_x,
step,
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()
m = 1
k0 = 1
x0 = x[int(N / 2)]
sig = 1
Psi_x = gauss_init(x, k0, x0=x0, d=sig)
V_x = np.zeros(N)
sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m)
# plt.plot(x,sch.mod_square_x(r=True))
# plt.show()
E = energy(k0, hbar, m)
Es = sch.energy()
print("theoretical energy", E)
print("additional theoretical energy", energy2(k0, hbar, m, sig))
print("simulated energy", Es)
print("diff", Es - E)
hbarChange(1, 15, 0.2)
mChange(1, 15, 0.2)
sigChange(1, 10, 0.2)
kChange(-5, 5, 0.1)
Nchange([9, 10, 11, 12, 13])
k0 = 2 x0 = int(N / 4) * dx sig = 8 bar_amp = 5 L = 20 x1 = (N / 2) * dx x2 = x1 + (L * dx) Psi_x = gauss_init(x, k0, x0=x0, d=sig) V_x = barrier(x, bar_amp, x1, x2) sch = Schrodinger(x, Psi_x, V_x, hbar=hbar, m=m, args=x1) print(sch.energy()) dt = 0.001 step = 100 finalt = 50 c = Constants(bar_amp, dt, dx, k0) # plt.plot(x, sch.psi_squared) # plt.plot(x, V_x) # plt.show() # a = Animate(sch, V_x, step, dt) # a.make_fig() ######Testing Impedence
dt = 0.01
step = 50
ft = 34
Ns = int(ft / (dt * step))
print(dt * Ns * step)
print("Diffusion", dt / (dx**2))
print("vdt", A * dt)
print("kdx", k_init * dx)
sch = Schrodinger(x, psi_init, V_x, k, hbar=hbar, m=m, t=t)
E = (hbar**2) * (k_init**2 + 1 / (4 * sig**2)) / (2 * m)
print("Energy", E)
print("Energy_sim", sch.energy())
print("Lenght", L)
# print("Theory", t_theory(L, A, E))
# plt.plot(x, sch.psi_squared)
# plt.plot(x, V_x)
# plt.show()
#
# a = Animate(sch, V_x, step, dt)
# a.make_fig()
################### Testing
t_list = []
for i in range(0, Ns):
t += dt * step
t_list.append(t)