A spatially indirect exciton in vertically coupled quantum dots is considered with the use of 1/Q-expansion, where Q is the dimensionless quantum parameter determined by the ratio of characteristic Coulomb energy of electron-hole interaction to the energy of one-particle transition in a confining potential. Analytical expressions for the energies and the wave functions are derived. They are asymptotically exact when Q 1 and the parameter of separation of quantum dots d is much larger than the size of a direct exciton a * B . It is shown, however, that even the first four terms in the 1/Q-expansion provide one percent accuracy for the energies of relative motion in the ground and the first excited states of the exciton for Q 2 and d a * B . It is also shown that the Padé summation of the first four terms in the 1/Q-expansion provides accuracy no worse than 5% even for Q ∼ 0.2. We use the perturbation theory with respect to Coulomb interaction to calculate the energies for smaller values of Q and thus obtain analytical expressions for them in the whole range of variation of the parameter Q. δ=5 0.01 0.1 200 150 100 50 0 ε n ,n 1 2 n =0, n =0 1 2 n =1, n =0 1 2 Q
Reduced energies ε n 1 ,n 2 versus the quantum parameter Q. The solid curves represent the numerical solution of Eq. ( 10), the results of Padé approximation are represented by dots.