## Duke Mathematical Journal

### Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields

#### Article information

Source
Duke Math. J., Volume 93, Number 3 (1998), 535-574.

Dates
First available in Project Euclid: 19 February 2004

https://projecteuclid.org/euclid.dmj/1077231105

Digital Object Identifier
doi:10.1215/S0012-7094-98-09319-X

Mathematical Reviews number (MathSciNet)
MR1626727

Zentralblatt MATH identifier
0948.35091

#### Citation

Iwatsuka, Akira; Tamura, Hideo. Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields. Duke Math. J. 93 (1998), no. 3, 535--574. doi:10.1215/S0012-7094-98-09319-X. https://projecteuclid.org/euclid.dmj/1077231105

#### References

• [1] Y. Aharonov and A. Casher, Ground state of a spin-$1\over 2\$charged particle in a two-dimensional magnetic field, Phys. Rev. A (3) 19 (1979), no. 6, 2461–2462.
• [2] Y. Colin de Verdière, L'asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys. 105 (1986), no. 2, 327–335.
• [3] H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators with application to quantum mechanics and global geometry, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1987.
• [4] L. Erdős, Ground-state density of the Pauli operator in the large field limit, Lett. Math. Phys. 29 (1993), no. 3, 219–240.
• [5] L. Erdős, Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals, Partial Differential Operators and Mathematical Physics (Holzhau, 1994), Oper. Theory Adv. Appl., vol. 78, Birkhäuser, Basel, 1995, pp. 127–132.
• [6] I. C. Gohberg and M. G. Kreĭ n, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969.
• [7] I. Shigekawa, Spectral properties of Schrödinger operators with magnetic fields for a spin $\frac12$ particle, J. Funct. Anal. 101 (1991), no. 2, 255–285.
• [8] A. V. Sobolev, Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field perturbed by an attenuating electric field, I, vol. 35, 1986, pp. 2201–2211.
• [9] A. V. Sobolev, On the Lieb-Thirring estimates for the Pauli operator, Duke Math. J. 82 (1996), no. 3, 607–635.
• [10] S. N. Solnyshkin, Asymptotic behavior of the energy of bound states of the Schrödinger operator in the presence of electric and homogeneous magnetic fields, vol. 5, 1986, pp. 297–306.
• [11] H. Tamura, Asymptotic distribution of eigenvalues for Schrödinger operators with homogeneous magnetic fields, Osaka J. Math. 25 (1988), no. 3, 633–647.