The Bloch equations when T1 = T2

The Bloch equations with relaxation times equal, i.e., T-1 = T-2, can be reduced to the spinor equation of motion ( or Zakharov - Shabat eigenvalue problem). The response to a complex, time- varying driving field can be expressed essentially as a Laplace transform of the solution to the spinor equation. This enables, in many cases, closed- form expressions for the response to be obtained, when closed- form solutions exist for the corresponding spinor equation. It enables the 'inversion' of the Bloch equations to produce relaxation- selective driving fields, i. e., the calculation of the driving field needed to produce a target response, specified as a function of relaxation rate.