We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj(g,T) of the operator - d2/dx2 + x2 + gVT(x) with V T(x) = x4 when |x|≤T and VT(x) = T 4 when |x| > T. The functions λj(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schrödinger series for every g>0.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics