The 2D Schrödinger equation for a neutral pair in a constant magnetic field

Arne Jensen; Shu Nakamura

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 4, page 387-410
  • ISSN: 0246-0211

How to cite

top

Jensen, Arne, and Nakamura, Shu. "The 2D Schrödinger equation for a neutral pair in a constant magnetic field." Annales de l'I.H.P. Physique théorique 67.4 (1997): 387-410. <http://eudml.org/doc/76773>.

@article{Jensen1997,
author = {Jensen, Arne, Nakamura, Shu},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Schrödinger operator; magnetic field; absolutely continuous spectrum},
language = {eng},
number = {4},
pages = {387-410},
publisher = {Gauthier-Villars},
title = {The 2D Schrödinger equation for a neutral pair in a constant magnetic field},
url = {http://eudml.org/doc/76773},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Jensen, Arne
AU - Nakamura, Shu
TI - The 2D Schrödinger equation for a neutral pair in a constant magnetic field
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 67
IS - 4
SP - 387
EP - 410
LA - eng
KW - Schrödinger operator; magnetic field; absolutely continuous spectrum
UR - http://eudml.org/doc/76773
ER -

References

top
  1. [1] N.W. Ashcroft and N.D. Mermin, Solid state physics, Holt, Rinehart and Winston, New York1976. Zbl1107.82300
  2. [2] J. Avron, I. Herbst and B. Simon, Separation of center of mass in homogeneous magnetic fields, Ann. Physics, Vol. 114, 1978, pp. 431-451. Zbl0409.35027MR507741
  3. [3] Ph. Briet, J.M. Combes and P. Duclos, Spectral stability under tunneling, Comm. Math. Phys., Vol. 126, 1989, pp. 133-156. Zbl0702.35189MR1027916
  4. [4] Ph. Briet, J.M. Combes and P. Duclos, Spectral stability under tunneling for Schrödinger operators, Symposium "Partial Differential Equations" Holzau 1988 (B.-W. Schulze and H. Triebel, eds), Teubner-Texte zur Mathematik, Vol. 112, Teubner, Leipzig, 1989, pp. 42-51. Zbl0686.35086MR1105798
  5. [5] H.L. Cycon, R.G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts and Monographs in Physics, Springer-Verlag, 1987. Zbl0619.47005
  6. [6] B. Helffer, Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Mathematics, Vol. 1336, Springer-Verlag, Berlin, 1988. Zbl0647.35002MR960278
  7. [7] B. Helffer, On spectral theory for Schrödinger operators with magnetic potentials, Spectral and scattering theory and applications (K. Yajima, ed.), Advanced Studies in Pure Mathematics, Vol. 23, Kinokuniya, Tokyo, 1994, pp. 113-141. Zbl0816.35100MR1275398
  8. [8] I.W. Herbst, Translation invariance of N-particle Schrödinger operators in homogeneous magnetic fields, Mathematical methods and applications of scattering theory (J. A. DeSanto, A. W. Sáenz, and W. W. Zachary, eds.), Lecture Notes in Physics, Vol. 130, Springer-Verlag, 1980, pp. 169-174. Zbl0481.35036
  9. [9] T. Kato, Perturbation theory for linear operators, second ed., Die Grundlehren der Mathematischen Wissenschaften, Vol. 132, Springer-Verlag, Berlin, Heidelberg, New York, 1976. Zbl0342.47009MR407617
  10. [10] W. Kirsch and B. Simon, Comparison theorems for the gap of Schrödinger operators, J. Funct. Anal., Vol. 75, 1987, pp. 396-410. Zbl0661.35062MR916759
  11. [11] I. Laba, Multiparticle quantum systems in constant magnetic fields, Preprint, UCLA, 1995. MR1487921
  12. [12] H. Matsumoto, Quadratic Hamiltonians and associated orthogonal polynomials, J. Function. Anal., Vol. 136, 1996, pp. 214-225. Zbl0966.33004MR1375159
  13. [13] M. Reed and B. Simon, Methods of modern mathematical physics. IV: Analysis of operators, Academic Press, New York, 1978. Zbl0401.47001MR493421
  14. [14] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S.), Vol.7, 1982, pp. 447-526. Zbl0524.35002MR670130
  15. [15] E. Skibsted, On the asymptotic completeness for particles in constant electromagnetic fields, Preprint, Department of Mathematics, Aarhus University, 1995. MR1380998
  16. [16] H.F. Weinberger, Variational methods for eigenvalue approxiation, CBMS, Vol. 15, SIAM, Philadelphia, 1974. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.