A method is presented for the calculation of tight upper and lower bounds for the energy eigenvalues of the Schr\"odinger equation. The method is based on a rational functional approximation for the series expansion of the solution of the Riccati equation for the logarithmic derivative of the wave function. Specific applications for one-dimensional anharmonic oscillators and for the Yukawa potential are given, and the present results are compared with those obtainable by other procedures.
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Fernández et al. (1989) studied this question.
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