Eigenstates of the potential V(x) = A2x2 + A4x4 + A6x6: state-dependent diagonalization method

We apply the state-dependent diagonalization method to study the eigenstates of quartic-sextic anharmonic oscillators (A2 > 0, A4 > 0 and A6 > 0) and double-well oscillators (A2 < 0, A4 > 0 and A6 = 0). This method is shown to be efficient for calculating energy eigenvalues and eigenfunctions; in particular, for the highly excited states. For a wide range of parameters, each of the first one thousand eigenstates of these systems can be accurately determined by diagonalizing matrices of dimension less than 220.