Abstract
The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.
| Original language | English |
|---|---|
| Pages (from-to) | 117-124 |
| Number of pages | 8 |
| Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |
| Volume | 216 |
| Issue number | 1-5 |
| DOIs | |
| Publication status | Published - Jun 17 1996 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cite this
The hydrogen atom in strong electric fields : Summation of the weak field series expansion. / Hiraizumi, Ken Ichi; Ohshima, Yoshihisa; Suzuki, Hiroshi.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 216, No. 1-5, 17.06.1996, p. 117-124.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The hydrogen atom in strong electric fields
T2 - Summation of the weak field series expansion
AU - Hiraizumi, Ken Ichi
AU - Ohshima, Yoshihisa
AU - Suzuki, Hiroshi
PY - 1996/6/17
Y1 - 1996/6/17
N2 - The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.
AB - The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.
UR - http://www.scopus.com/inward/record.url?scp=0010803614&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0010803614&partnerID=8YFLogxK
U2 - 10.1016/0375-9601(96)00243-5
DO - 10.1016/0375-9601(96)00243-5
M3 - Article
AN - SCOPUS:0010803614
VL - 216
SP - 117
EP - 124
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 1-5
ER -