An asymptotic functional-integral solution for the Schrödinger equation with polynomial potential

A functional integral representation for the weak solution of the Schrödinger equation with a polynomially growing potential is proposed in terms of an analytically continued Wiener integral. The asymptotic expansion in powers of the coupling constant λ of the matrix elements of the Schrödinger group is studied and its Borel summability is proved. © 2009 Elsevier Inc. All rights reserved.