Bound States of the Magnetic Schrödinger Operator
Nicolas Raymond
Université de Rennes, France
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| FrontmatterDownload pp. i–v | |
| Prolégomènes francophonesDownload pp. vii–viii | |
| PrefaceDownload pp. ix–x | |
| ContentsDownload pp. xi–xiv | |
| 0 | A magnetic storypp. 1–21 |
| Part 1 Methods and examplesp. 23 | |
| 1 | Elements of spectral theorypp. 25–56 |
| 2 | Examplespp. 57–85 |
| 3 | First semiclassical examplespp. 87–96 |
| 4 | From local models to global estimatespp. 97–115 |
| 5 | Birkhoff normal form in dimension onepp. 117–128 |
| Part 2 Main theoremsp. 129 | |
| 6 | Spectral reductionspp. 131–147 |
| 7 | Magnetic wells in dimension twopp. 149–160 |
| 8 | Boundary magnetic wells in dimension threepp. 161–175 |
| 9 | Waveguidespp. 177–194 |
| 10 | On some connected non-linear problemspp. 195–200 |
| Part 3 Spectral reductionsp. 201 | |
| 11 | Electric Born–Oppenheimer approximationpp. 203–220 |
| 12 | Magnetic Born–Oppenheimer approximationpp. 221–233 |
| 13 | Examples of magnetic WKB constructionspp. 235–243 |
| Part 4 Magnetic wells in dimension twop. 245 | |
| 14 | Vanishing magnetic fields in dimension twopp. 247–259 |
| 15 | Non-vanishing magnetic fieldspp. 261–272 |
| 16 | Semiclassical non-linear magnetic eigenvaluespp. 273–285 |
| Part 5 Boundary magnetic wells in dimension threep. 287 | |
| 17 | Magnetic half-spacepp. 289–304 |
| 18 | Magnetic wedgepp. 305–312 |
| 19 | Magnetic conepp. 313–325 |
| Part 6 Waveguidesp. 327 | |
| 20 | Magnetic effects in curved waveguidespp. 329–342 |
| 21 | Spectrum of thin triangles and broken waveguidespp. 343–350 |
| 22 | Non-linear dynamics in bidimensional waveguidespp. 351–359 |
| Bibliographypp. 361–378 | |
| Indexpp. 379–380 |