Unified treatment of even and odd anharmonic oscillators of arbitrary degree.
We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behavior of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.
Jentschura
Ulrich D
UD
Department of Physics, Missouri University of Science and Technology, Rolla Missouri 65409-0640, USA.
Surzhykov
Andrey
A
Zinn-Justin
Jean
J