A method described previously for obtaining upper and lower bounds for the eigenenergies of the Schr\"odinger equation for parity-invariant and central potentials is extended and applied to asymmetric one-dimensional potentials. The procedure consists of transforming the Schr\"odinger equation into a Ricati one for the logarithmic derivative of the wave function. The solution of the latter equation is approached by a series of Pad\'e approximants. Approximate eigenenergies are obtained from the roots of associated determinants, and such roots are proved, in some cases, to be upper or lower bounds to the actual eigenenergies. The method is illustrated by calculations for several model potentials and the results compared with those obtained by alternative procedures.
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Fernández et al. (1989) studied this question.