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