DELTA-EXPANSION FOR THE SUPERPOTENTIAL

We use the δ expansion to solve the Riccati equation for the superpotential W(x) involved in factorization of the Hamiltonian for the anharmonic oscillator with V(x)=λx2+2δ. We solve for the superpotential as a power series in δ. We find that potentials of the form x2n are well approximated by Padé approximants to the first few terms in the δ expansion. By considering the hierarchy of isospectral potentials related to the original potential by supersymmetry and factorization we show how to construct approximate wave functions and energy eigenvalues of the ground state and all the excited states. Thus the δ expansion allows for an approxomate algebraic solution of the anharmonic oscillator problem. © 1990.