Little Summary of Bloch Equations and Magnetization

• Although, the number of spins is conserved, $\vec{M}$ is not conserved at all times.
  
  

• can't have $\vert\vec{M}\vert$ exceed $M_{0}$ which implies that $T_{1}$ is always going to be longer than $T_{2}$.

• Have solutions for transverse and longitudinal magnetization
  

  $$M_{z}(t) = M_{z}(0) e^{-t/T_{1}} + M_{0} (1 - e^{-t/T_{1}})$$

  $$M_{+}(t) = e^{-i\omega_{0}t- t/T_{2}} M_+(0)$$ (4.10)

  
  
  where we are using the complex representation from Chapter 2 to characterize the transverse magnetization.

• Let's do an (IN CLASS QUESTION)