Some estimates concerning the Zeeman effect
Cupała, Wiesław
Studia Mathematica, Tome 104 (1993), p. 13-23 / Harvested from The Polish Digital Mathematics Library
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The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:215979 
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     title = {Some estimates concerning the Zeeman effect},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {13-23},
     zbl = {0811.35023},
     language = {en},
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Cupała, Wiesław. Some estimates concerning the Zeeman effect. Studia Mathematica, Tome 104 (1993) pp. 13-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p13bwm/

[00000] [1] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York 1974. | Zbl 0278.60039

[00001] [2] N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris 1971. | Zbl 0213.04103

[00002] [3] M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. of Math. 106 (1977), 93-100. | Zbl 0362.47006

[00003] [4] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207. | Zbl 0312.35026

[00004] [5] E. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, unpublished. | Zbl 0445.58029

[00005] [6] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. | Zbl 0008.11301

[00006] [7] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, 1978. | Zbl 0401.47001

[00007] [8] G. W. Rosenblum, The distribution of the discrete spectrum of singular differential operators, Dokl. Akad. Nauk SSSR 202 (1972), 1012-1015 (in Russian).

[00008] [9] B. Simon, Schrödinger operators with singular magnetic vector potentials, Math. Z. 131 (1973), 361-370. | Zbl 0277.47006

[00009] [10] B. Simon, Functional Integration and Quantum Physics, Academic Press, 1979. | Zbl 0434.28013