Proceedings of the Japan Academy, Series A, Mathematical Sciences

Error bounds on the Trotter-Kato product formula of relativistic Schrödinger operators with electromagnetic fields

Atsushi Doumeki

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Abstract

We give error bounds of the Trotter-Kato product formula of relativistic Schrödinger operators $\sqrt{(i \partial_x - a(x))^2 + 1} - 1 + V(x)$, where $B(x) = \nabla \times a(x)$ is bounded and $V(x)$ behaves like $|x|^{\rho}$, $\rho > 0$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 2 (2000), 7-12.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393579

Digital Object Identifier
doi:10.3792/pjaa.76.7

Mathematical Reviews number (MathSciNet)
MR1752815

Zentralblatt MATH identifier
0954.47035

Subjects
Primary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords
Trotter-Kato product formula relativistic Schrödinger operators operator-norm estimates.

Citation

Doumeki, Atsushi. Error bounds on the Trotter-Kato product formula of relativistic Schrödinger operators with electromagnetic fields. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 2, 7--12. doi:10.3792/pjaa.76.7. https://projecteuclid.org/euclid.pja/1148393579


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References

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