Edwin Barnes, S. Das Sarma
Analytical solutions to the time-dependent Schr\"odinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schr\"odinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.
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http://arxiv.org/abs/1206.0297
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