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A variational calculus method is applied for hydrogen-like impurities statesand exciton states in AlGaAs/GaAs quantum wells within the effective massesapproach. The hamiltonian is separated into radial and transversal parts to beconsidered and optimized using trial wavefunctions. The results satifsy thewell-known cases of three-dimentional and two-dimentional hydrogen. The donorand exciton bound energy is shown to decrease while widthening the quantumwell. The non-symmetrical donor position also decreases the bound energy.

Application of the variations calculus on energy spectra of shallow hydrogen-like impurities and excitons in GaAs/AlGaAs quantum wells