Some estimates concerning the Zeeman effect

• Autorzy: Wiesław Cupała
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

estimation of eigenvalues; Schrödinger operator

Kategorie tematyczne

• 35P15: Estimation of eigenvalues, upper and lower bounds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 1
• Strony: 13-23

Daty

wydano

1993

otrzymano

1991-04-23

poprawiono

1992-06-08

poprawiono

1993-02-08

Twórcy

autor

Wiesław Cupała

• Institute of Mathematics, Polish Academy of Sciences, Wrocław, Branch, Kopernika 18, 51-617 Wrocław, Poland.

Bibliografia

• [1] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York 1974.
• [2] N. Bourbaki, Groupes et Algèbres de Lie, Hermann, Paris 1971.
• [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.
• [4] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207.
• [5] E. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, unpublished.
• [6] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216.
• [7] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, 1978.
• [8] G. W. Rosenblum, The distribution of the discrete spectrum of singular differential operators, Dokl. Akad. Nauk SSSR 202 (1972), 1012-1015 (in Russian).
• [9] B. Simon, Schrödinger operators with singular magnetic vector potentials, Math. Z. 131 (1973), 361-370.
• [10] B. Simon, Functional Integration and Quantum Physics, Academic Press, 1979.