[en] The ¹²C nucleus as three finite structurelesse alpha particles interacting through phenomenological potentials due to Ali and Bodmer is represented. These potentials are angular-momentum dependent and reproduce the experimental phase shifts delta₀, delta₂ and delta₄ associated with α-α scattering. The wave functions expanded in terms of harmonic-oscillator (HO) states which are translationally invariant, completely symmetric and have defined total angular momentum. The coefficients of the expansion, as well as the oscillator frequency, are treated as variational parameters. It was checked the quality of the wave functions for the excited O⁺ state and for the 2⁺ states derived here. The test is made by calculating the spectra, inelastic form factors for electron scattering, and transition widths for transitions 2⁺→O⁺ (electromagnetic) and O⁺→O⁺ (pair production)