Link between the strong-coupling and the weak-coupling asymptotic perturbation expansions for the quartic anharmonic oscillator

摘要

For eigenvalues E(beta) of the Hamiltonian of the quartic anharmonic oscillator we give a representation which reproduces two well known limiting cases from the theory of the anharmonic oscillator expansions: the weak-coupling asymptotic perturbation and the convergent strong coupling. We give an estimation of the radius of convergence of the strong-coupling expansion for the ground-state eigenvalue. [References: 18]