2007/08/16 by David Leonard, David Léonard, Leonard, David +2
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #High-Energy Particle Collisions Research #Numerical methods for differential equations #Quantum Chromodynamics and Particle Interactions #Quantum Physics (quant-ph) #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.0708.2201
23 pages, 12 figures
arxiv created 2007/08/16 · openalex publication_date 2007/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides the energy eigenvalues directly however in the third method we tune the wavefunctions to achieve the correct large x behaviour. This tuning technique allows us to determine the energy eigenvalues up to an arbitrary level of accuracy with remarkable efficiency. We give numerical evidence to explain this behaviour. We also refine the modified Borel summation technique to improve its accuracy. The main sources of error are investigated with reasonable error corrections calculated.