Accurate eigenvalues and eigenfunctions for quantum-mechanical anharmonic oscillators

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Abstract
The representation of the Taylor expansion of the logarithmic-derivative of the wavefunction by means of a Pade approximant, followed by an appropriate quantization condition, proves a powerful way of obtaining accurate eigenvalues of the Schrodinger equation. In this paper we investigate in detail some of the interesting features of this approach, termed Riccati-Pade method (RPM), by means of its application to anharmonic oscillators. We analyse the occurrence of many roots in the neighborhoods of the physical eigenvalues in the weak-coupling regime, and also obtain accurate coefficients of the strong-coupling expansion. We finally investigate the global and the local accuracy of the RPM eigenfunctions.