APPLICATION OF THE EIGENVALUE MOMENT METHOD TO IMPORTANT ONE-DIMENSIONAL QUANTUM-SYSTEMS

We study the effectiveness of the eigenvalue moment method as applied to various one-dimensional quantum problems which have appeared in the literature. Of particular interest are the radial potential problems (including angular momentum effects) -Ze2/(r + beta) and r2 + lambdar2/(1 + gr2) studied by De Meyer and Vanden Berghe (and more recently by Femandez), and Witwit, respectively. We also examine the potentials 1/2x2 +/- gx4/(1 + alphagx2), exhaustively studied by Auberson and Boissiere. Finally, we examine the one-dimensional regulated Bohr atom with potential -Z/(Absolute value of x + alpha), well studied by Loudon, and Haines and Roberts.