Abstract
The Bloch equations with relaxation times equal, i.e., T1 = T2, 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.
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