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A general treatment of the quantal time-dependent coupled oscillators inpresence of the variable magnetic field is presented. The treatment is based onthe use of an alternative canonical transformations, time-dependent unitarytransformations and the invariant methods. Exact wave functions forSchr\"{o}dinger equations of this system are constructed.We applied our theoryto a particular case and, co,sequently, showed that our results recovers to theperviously known one.

An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field