Solving the anharmonic oscillator: Tuning the boundary condition.

Leonard, D.; Mansfield, P.

Abstract

We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x2M potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary condition by generating a power series expansion of the wavefunction in x and applying a modified Borel resummation technique to obtain the large x behaviour. The process allows us to calculate energy eigenvalues to an arbitrary level of accuracy. High degrees of precision are achieved even with modest computing power. Our technique extends to all levels of excitation and produces the correct solution to the double well oscillators even though they are dominated by non-perturbative effects.

Citation

Leonard, D., & Mansfield, P. (2007). Solving the anharmonic oscillator: Tuning the boundary condition. Journal of Physics A: Mathematical and Theoretical, 40(33),

• Journal Article Type: Article
• Publication Date: 2007-03
• Deposit Date: Nov 19, 2010
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Publisher: IOP Publishing
• Volume: 40
• Issue: 33
• Public URL: https://durham-repository.worktribe.com/output/1515566
• Publisher URL: http://iopscience.iop.org/1751-8121/40/33/020/