Tight bounds to the Schrodinger equation eigenvalues
Francisco Marcelo Fernández, G. I. Frydman, Eduardo A. Castro · Journal of Physics A Mathematical and General · 1989
Increasing tight upper and lower bounds to the Schrodinger equation eigenvalues are obtained from the Riccati equation for the logarithmic derivative of the wavefunction. The solution of this non-linear equation is written as a Pade approximant and the bounds are given by the roots of a sequence of determinants. Numerical results are shown for the anharmonic and quartic oscillators.