| Summary: | Using the Hubbard representation for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>U</mi> <mo>(</mo> <mn>2</mn> <mo>)</mo> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of nonlinear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. A physical model with the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomenon.
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