|
| related topics |
| {equation, function, exp} |
| {energy, state, states} |
| {error, code, errors} |
|
Solving the Anharmonic Oscillator: Tuning the Boundary Condition
David Leonard, Paul Mansfield
abstract: We outline a remarkably efficient method for generating solutions to quantum
anharmonic oscillators with an x^{2M} 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0703262
- categories:
- quant-ph hep-th
- comments:
- 10 pages, 4 figures. V3 contains minor changes made before final
publication
- doi:
- 10.1088/1751-8113/40/33/020
- arxiv_id:
- quant-ph/0703262
- journal_ref:
- J.Phys.A40:10291-10300,2007
- created:
- 2007-03-28
- updated:
- 2007-08-09
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