The binding energy of excitons and X + and X - trions in one-dimensional systems

The exciton and trion states in semiconductor quantum wires are treated by the variational method. Simple trial functions provide an adequate precision of the calculation over a wide region of wire radii, with an arbitrary relation between the effective masses of charge carriers. The precision of the results obtained by the variational method is checked by numerical diagonalization of the Hamiltonian of excitons and positively and negatively charged trions. The asymptotic behavior of the binding energies of excitons and trions in narrow quantum wires is established in the analytical form. The structure of the excited X (+) trion states is analyzed in the context of the adiabatic approximation.