Rescaled Perturbation Theory
Abstract
A nonperturbative method that can go beyond the weak coupling perturbation theory is introduced. The essential idea is to formulate a set of exact differential equations as a function of coupling strength g. Unlike other resummation methods in which information on higherorder terms is necessary, we only need a leadingorder perturbative formula in every step to reach a large value of g. The method is applied to the quantum anharmonic oscillator and quantum doublewell potential in one dimension. Both are known to have divergent series in the weak coupling perturbation and the latter is not Borelsummable. Our method is shown to work well from the weak coupling to the strong coupling for the energy eigenvalues and the wave functions. The method is also applied successfully to a system with a timedependent external field.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 December 2010
 DOI:
 10.1143/PTP.124.1097
 arXiv:
 arXiv:1010.6125
 Bibcode:
 2010PThPh.124.1097H
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 High Energy Physics  Theory
 EPrint:
 8 pages, 4 figures