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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Professor Emeritus Paul Mansfield

D. Leonard & P. Mansfield (2007). Solving the anharmonic oscillator: Tuning the boundary condition. Journal of Physics A: Mathematical and Theoretical 40(33): 10291.

Author(s) from Durham


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.