Coupled Spins¶

In [9]:

import numpy as np
import matplotlib.pyplot as plt
np.set_printoptions(precision=2, suppress=True)

import numpy as np import matplotlib.pyplot as plt np.set_printoptions(precision=2, suppress=True)

In [10]:

from tins import spinsys, mesolve
import numpy as np

from tins import spinsys, mesolve import numpy as np

In [11]:

I1, I2 = spinsys(0.5, 0.5)

I1, I2 = spinsys(0.5, 0.5)

In [12]:

j_ham = -2 * np.pi * 200 * I1.z
j_ham += 2 * np.pi * 200 * I2.z
j_ham += 2 * np.pi * 40 * (I1.z @ I2.z + I1.x @ I2.x + I1.y @ I2.y)

j_ham = -2 * np.pi * 200 * I1.z j_ham += 2 * np.pi * 200 * I2.z j_ham += 2 * np.pi * 40 * (I1.z @ I2.z + I1.x @ I2.x + I1.y @ I2.y)

In [13]:

j_ham

j_ham

Out[13]:

array([[   62.83+0.j,     0.  +0.j,     0.  +0.j,     0.  +0.j],
       [    0.  +0.j, -1319.47+0.j,   125.66+0.j,     0.  +0.j],
       [    0.  +0.j,   125.66+0.j,  1193.81+0.j,     0.  +0.j],
       [    0.  +0.j,     0.  +0.j,     0.  +0.j,    62.83+0.j]])

In [14]:

inital_state = I1.x + I2.x
detect = (I1.x + I2.x) + 1j * (I1.y + I2.y)
time = np.linspace(0, 1, 2000)
out = mesolve(start=inital_state, detect=detect, ham=j_ham, time=time)

ft = np.fft.fftshift(np.fft.fft(out * np.exp(-10 * time)))

inital_state = I1.x + I2.x detect = (I1.x + I2.x) + 1j * (I1.y + I2.y) time = np.linspace(0, 1, 2000) out = mesolve(start=inital_state, detect=detect, ham=j_ham, time=time) ft = np.fft.fftshift(np.fft.fft(out * np.exp(-10 * time)))

In [20]:

fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(ft.real)
plt.show()

fig, ax = plt.subplots(figsize=(6, 3)) ax.plot(ft.real) plt.show()

Q1¶

1. What does the spectrum look like if the two heteronuclear spins are coupled?

In [ ]:

# your answer here

# your answer here

Q2¶

Simulate the spectrum in presence of (a) Dipole dipole coupling and (b) J-coupling + Dipole dipole coupling

In [16]:

d_ham = -2 * np.pi * 200 * I1.z
d_ham += 2 * np.pi * 200 * I2.z
d_ham += 2 * np.pi * 100 * (2 * I1.z @ I2.z - I1.x @ I2.x - I1.y @ I2.y)

d_ham = -2 * np.pi * 200 * I1.z d_ham += 2 * np.pi * 200 * I2.z d_ham += 2 * np.pi * 100 * (2 * I1.z @ I2.z - I1.x @ I2.x - I1.y @ I2.y)

In [ ]:

# continue you answer here

# continue you answer here

In [21]:

fig, ax = plt.subplots(figsize=(6, 3))
# contine your answer here

fig, ax = plt.subplots(figsize=(6, 3)) # contine your answer here

In [ ]: