ACCURATE EIGENVALUES AND EIGENFUNCTIONS FOR QUANTUM-MECHANICAL ANHARMONIC-OSCILLATORS

The representation of the Taylor expansion of the logarithmic-derivati ve 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 in vestigate in detail some of the interesting features of this approach, termed Riccati-Pade method (RPM), by means of its application to anha rmonic oscillators. We analyse the occurrence of many roots in the nei ghborhoods of the physical eigenvalues in the weak-coupling regime, an d also obtain accurate coefficients of the strong-coupling expansion. We finally investigate the global and the local accuracy of the Rpm ei genfunctions.