Quantum Mechanics for Engineers 

© Leon van Dommelen 

D.75 Solving the NMR equations
To solve the two coupled ordinary differential equations for the spin
up and down probabilities, first get rid of the time dependence of the
righthandside matrix by defining new variables and by
Then find the eigenvalues and eigenvectors of the now constant matrix.
The eigenvalues can be written as , where
is the resonance factor given in the main text. The solution is
then
where and are the eigenvectors. To find the
constants and , apply the initial conditions
and and clean
up as well as possible, using the definition of the resonance factor
and the Euler formula.
It's a mess.