Abstract
In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin–orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.
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