Modified δ expansion for nonlinear problems

Abstract

A recently proposed perturbative technique called the δ expansion is modified to improve the convergence properties of the method considerably. The expansion method consists of replacing a nonlinear term like Φ 2 p by ℋ ( Φ/ℋ ) 2(1+ δ ) and then treating δ as a small parameter where ℋ is used to construct a suitable zero-order approximation. It is shown that excellent numerical results are obtained by starting with a properly chosen ℋ . The approach is applied to a zero-dimensional field theory and to the solution of the one-dimensional stationary Schrödinger equation.