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.
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Fernández et al. (1989) studied this question.
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