Global solution of the cubic oscillator

The eigenstates of a real or complex cubic anharmonic oscillator are investigated using original and alternative methods. The procedure consists of determining global solutions of the Schr\"odinger equation that comply with the pertinent boundary conditions and allows us to obtain, in a very simple way, the eigenenergies and eigenfunctions of the Hamiltonian. Scattering by a real cubic potential is investigated as a specific case.