The problem of exciton-exciton interaction in molecular crystals is discussed in terms of the stationary two-quantum excited states of an idealized one-dimensional crystal. If only a single molecular excited state is considered, the wave functions and energy levels of the two-quantum states may be obtained directly from those of the corresponding one-quantum problem with the proviso that the two excitons have different wave numbers. If in addition, a second molecular excited state is included, there can exist states in which two excitons remain bound to each other as they propagate through the crystal.
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R. E. Merrifield (1959) studied this question.