We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schr\"odinger equation exactly, discussing the limits of quasi-one-and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows us to extend the validity of our results to the case of tight traps and large scattering lengths.
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Idziaszek et al. (2005) studied this question.
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