Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials
One-dimensional Schrödinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized δ-like magnetic fields are combined with δ′-like perturbations of...
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Frontiers Media S.A.
2019-05-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2019.00070/full |
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doaj-f2c51480f7694d61bceed523efbccc552020-11-25T02:17:44ZengFrontiers Media S.A.Frontiers in Physics2296-424X2019-05-01710.3389/fphy.2019.00070437394Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric PotentialsYuriy GolovatyOne-dimensional Schrödinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized δ-like magnetic fields are combined with δ′-like perturbations of the electric potentials as well as localized rank-two perturbations. The limit results obtained heavily depend on zero-energy resonances of the electric potentials. In particular, the approximation for a wide class of point interactions in one dimension is obtained.https://www.frontiersin.org/article/10.3389/fphy.2019.00070/full1D Schrödinger operatormagnetic potentialzero-energy resonancehalf-bound stateshort range interactionpoint interaction |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuriy Golovaty |
| spellingShingle |
Yuriy Golovaty Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials Frontiers in Physics 1D Schrödinger operator magnetic potential zero-energy resonance half-bound state short range interaction point interaction |
| author_facet |
Yuriy Golovaty |
| author_sort |
Yuriy Golovaty |
| title |
Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials |
| title_short |
Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials |
| title_full |
Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials |
| title_fullStr |
Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials |
| title_full_unstemmed |
Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials |
| title_sort |
some remarks on 1d schrödinger operators with localized magnetic and electric potentials |
| publisher |
Frontiers Media S.A. |
| series |
Frontiers in Physics |
| issn |
2296-424X |
| publishDate |
2019-05-01 |
| description |
One-dimensional Schrödinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized δ-like magnetic fields are combined with δ′-like perturbations of the electric potentials as well as localized rank-two perturbations. The limit results obtained heavily depend on zero-energy resonances of the electric potentials. In particular, the approximation for a wide class of point interactions in one dimension is obtained. |
| topic |
1D Schrödinger operator magnetic potential zero-energy resonance half-bound state short range interaction point interaction |
| url |
https://www.frontiersin.org/article/10.3389/fphy.2019.00070/full |
| work_keys_str_mv |
AT yuriygolovaty someremarkson1dschrodingeroperatorswithlocalizedmagneticandelectricpotentials |
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1724885418687594496 |