Pulses¶

If you do not go into the rotating frame, you will need to consider a time dependent B1 field whenever you apply a pulse.

• Solve the evolution equation considering a circularly polarized and a linearly polarized B1 field.
• Show the Bloch-Siegert Shift numerically.
• How does this calculation change if you go to the rotating frame?

In [2]:

from tins import spinsys
import numpy as np
from scipy.linalg import expm
np.set_printoptions(precision=2, suppress=True)

from tins import spinsys import numpy as np from scipy.linalg import expm np.set_printoptions(precision=2, suppress=True)

In [3]:

I = spinsys(0.5)
start = I.z
detect = I.p

I = spinsys(0.5) start = I.z detect = I.p

In [4]:

def rf_circularly_polarized(amplitude, nu, t):
    return amplitude * (
        I.x * np.cos(2 * np.pi * nu * t) + I.y * np.sin(2 * np.pi * nu * t)
    )


def rf_linearly_polarized(amplitude, nu, t):
    return amplitude * (
        I.x * np.cos(2 * np.pi * nu * t) + I.y * np.sin(2 * np.pi * nu * t)
    ) # +... continue

def rf_circularly_polarized(amplitude, nu, t): return amplitude * ( I.x * np.cos(2 * np.pi * nu * t) + I.y * np.sin(2 * np.pi * nu * t) ) def rf_linearly_polarized(amplitude, nu, t): return amplitude * ( I.x * np.cos(2 * np.pi * nu * t) + I.y * np.sin(2 * np.pi * nu * t) ) # +... continue

In [5]:

# continue with the calculation for the solution to the time dependent equation 

# continue with the calculation for the solution to the time dependent equation

In [ ]: