Restricted Three Body Problem in Semiconductor Heterostructure

The three-body restricted problem for X (-) and X (+) trions when a spatially separated exciton and electron or hole are located in the parallel quantum wells (QW) is reduced to the 2D three body problem for the exciton and the projection of the electron or hole on the plane of the excitonic QW. In the limit of a large spatial separation of the QWs the eigenfunctions and energy spectrum for X (-) and X (+) trions are obtained analytically. The 2D Wigner crystallization of the trions in the coupled QWs is discussed.