PERTURBED FACTORIZATION OF THE SINGULAR ANHARMONIC-OSCILLATOR EIGENEQUATION

The perturbed-ladder-operator method is applied to the solution of the perturbed eigenequation dx(2))-[m(m+1)/x(2)]-b(2)x(2)+V(x)+Lambda}Psi (X)=0 where V(x)=b(1)(1/x)(2)+b(2)(1/x)(4)+... is a singular perturbat ion. This method, which is the extension of the Schrodinger-Infeld-Hul l factorization method within the perturbation scheme, provides closed form expressions of the perturbed eigenvalues and ladder functions, b y means of algebraic manipulations. As an illustrative application, an analytical solution of the spiked-harmonic-oscillator eigenequation { (d(2)/dx(2))-b(2)x(2)-(lambda/x(4))+E}Psi(X)=0 is worked out up to the second order of the perturbation, by considering specifically adapted m- and lambda-dependent perturbing and unperturbed potentials in orde r to tentatively avoid the known difficulties of convergence of the pe rturbation series. Closed form expressions of the lambda/x(4)-anharmon ic-oscillator energies are obtained in terms of the coupling constant lambda and the quantum number upsilon: results following from these ex pressions are compared with exact available values. (C) 1994 American Institute of Physics.