|
| related topics |
| {equation, function, exp} |
| {energy, state, states} |
| {temperature, thermal, energy} |
| {time, wave, function} |
| {state, phys, rev} |
| {bell, inequality, local} |
|
A new method for the solution of the Schrodinger equation
Paolo Amore, Alfredo Aranda, Arturo De Pace
abstract: We present a new method for the solution of the Schrodinger equation
applicable to problems of non-perturbative nature. The method works by
identifying three different scales in the problem, which then are treated
independently: An asymptotic scale, which depends uniquely on the form of the
potential at large distances; an intermediate scale, still characterized by an
exponential decay of the wave function and, finally, a short distance scale, in
which the wave function is sizable. The key feature of our method is the
introduction of an arbitrary parameter in the last two scales, which is then
used to optimize a perturbative expansion in a suitable parameter. We apply the
method to the quantum anharmonic oscillator and find excellent results.
- oai_identifier:
- oai:arXiv.org:quant-ph/0304043
- categories:
- quant-ph
- comments:
- 4 pages, 4 figures, RevTex4
- doi:
- 10.1088/0305-4470/37/10/014
- arxiv_id:
- quant-ph/0304043
- journal_ref:
- Journal of Physics A 37 (2004) 3515-3525
- created:
- 2003-04-04
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