Ao.Univ.-Prof. Dr.phil. Bernd Thaller

Professor - aktiv

Universität Graz
Naturwissenschaftliche Fakultät
Institut für Mathematik und Wissenschaftliches Rechnen
Mathematische Physik
Ort / PLZ
8010 Graz
Heinrichstrasse 36
+43 (0)316 380-5164
+43 (0)316 380-5171
+43 (0)316 380-9815

Auszeichnungen und Ehrungen

European Academic Software Award 2000,
European Academic Software Award 2004




"The Dirac Equation"
Monographie, pp. 357+XVII.
Texts and Monographs in Physics. W. Beiglböck, E. Lieb, W. Thirring (Hrsg.)
Springer Verlag, Berlin, Heidelberg, New York 1992

"Visual Quantum Mechanics - Selected Topics with computer generated movies of quantum mechanical phenomena"
Book/CD combination, Springer-Verlag New York 2000, ISBN 0-387-98929-3

"Advanced Visual Quantum Mechanics", Book/CD combination, Springer New York 2004, ISBN 0-387-20777-5

Journals and refereed contributions

On the high-energy behaviour of scattering phase shifts for Coulomb-like potentials,
in: J. Phys. A: Math. Gen. 13, 2659-2671 (1980),
with F. Gesztesy and W. Plessas

Born expansions for Coulomb-type interactions,
in: J. Phys. A: Math. Gen. 14, 639-657 (1981),
with F. Gesztesy

Potential scattering of Dirac particles,
in: J. Phys. A: Math. Gen. 14, 3067-3083 (1981)

Proper-time quantum mechanics and the Klein paradox,
in: Lettere al Nuovo Cimento 31, 439-444 (1981)

Spectral concentration in the nonrelativistic limit,
in: Physics Letters 116B, 155-157 (1982),
with F. Gesztesy and H. Grosse

Efficient method for calculating relativistic corrections for spin-1/2 particles,
in: Physical Review Letters 50, 625-628 (1983),
with F. Gesztesy and H. Grosse

A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles,
in: Ann. Inst. H. Poincare,e 40, 159-174 (1984),
with F. Gesztesy and H. Grosse

Remarks on the localization of Dirac particles,
in: Il Nuovo Cimento 82A, 222-228 (1984),
with S. Thaller

Relativistic corrections to bound-state energies for two-fermion systems,
in: Physical Review D30, 2189-2193 (1984),
with F. Gesztesy and H. Grosse

Particles in sperical electromagnetic radiation fields,
in: Physical Review A31, 2030-2037 (1985),
with H. Mitter

On the self-adjointness of Dirac operators with anomalous magnetic moment,
in: Proceedings of the AMS 94, 115-118 (1985),
with F. Gesztesy and B. Simon

First order relativistic corrections and spectral concentration,
in: Adv. Appl. Math. 6, 159-176 (1985),
with F. Gesztesy and H. Grosse

Asymptotic observables and Coulomb scattering for the Dirac equation,
in: Ann. Inst. H. Poincare,e 45, 147-171 (1986),
with V. Enss

Relativistic scattering theory for long-range potentials of the nonelectrostatic type,
in: Lett. Math. Phys. 12, 15-19 (1986)

Scattering of particles by long-range magnetic fields,
in: Annals of Physics 176, 159-180 (1987),
with M. Loss

Normal forms of an abstract Dirac operator and applications to scattering theory,
in: J. Math. Phys. 29, 249-257 (1988)

Short-range scattering in long-range magnetic fields: The relativistic case,
in: J. Diff. Eq. 73, 225-236 (1988),
with M. Loss

Scattering theory of a supersymmetric Dirac operator, in: "Differential Equations with Applications in Biology, Physics and Engineering", J. Goldstein, F. Kappel, W. Schappacher (Hrsg.), 313-326, Lecture notes in pure and applied mathematics, Vol. 133, Marcel Dekker, New York, Basel, Hong-Kong 1991.

A Criterion for Essential Self-Adjointness,
in: J. Op. Theory 31, 351-361 (1995)

Factorization of Degenerate Cauchy Problems
J.Op.Theory 36, 121-146 (1996)
with S. Thaller,

Optimal Heat Kernel Estimates for Schrödinger Operators with Magnetic Fields,
Commun. Math. Phys. 186 (1), 95-107 (1997)
with M. Loss

Quantum Mechanical Wavefunctions in 3D Visualized with AVS,
Computers in Physics, November/December 1996, pp. 558-566
with J. Pauschenwein

InterCall and the Visualization of Quantum Mechanical Wave Functions.
in "The InterCall Book", Trefry and Abbott (Eds), Analytica International, Perth, Australia, ISBN 0-646-35666-6, July 1998

The Visualization of Complex Functions, The Mathematica Journal 7(2), 163-180 (1998)

Semigroup Theory of Degenerate Cauchy Problems,
Semigroup Forum 62, 375-398 (2001)
with S. Thaller

Semirelativistic Wave Scattering, in: Scattering, P. Sabatier and E.R. Pike (eds), Academic Press 2002, ISBN 0-12-613760-9

Contributions to books and proceedings

Scattering from magnetic fields,
in "Recent Developments in Mathematical Physics", Proceedings of the XXVI Int. Universitätswochen für Kernphysik 1987, Schladming, H. Mitter and L. Pittner eds., Springer Verlag Berlin, Heidelberg, New York (1987),
with M. Loss

Dirac particles in magnetic fields,
in: "Recent Developments in Quantum Mechanics", A. Boutet de Monvel et al. (Hrsg.), 351-366, Kluwer Academic Publishers 1991

Norm Estimates for Schrödinger Semigroups with Magnetic Fields,
in: Proceedings of the 7th International Colloquium on Differential Equations, Plovdiv, Bulgaria (1996), Ed. D. Bainov, VSP BV Utrecht 1997
with M. Loss

The Weyl theorem (on operator perturbation), Encyclopeadia of Mathematics, Supplement II, page 507. M. Hazewinkel (ed.), Kluwer Academic Publishers 2000, ISBN 0-7923-6114-8.

The Dirac Operator, in: Relativistic Electronic Structure Theory, Part 1. Fundamentals, P. Schwerdtfeger, ed., p.23-106,. Elsevier 2002, ISBN 0444 512497

Technical Reports

Teilchen in elektromagnetischen Kugelwellenfeldern
Institut f. Theoret. Physik, Universität Graz, 1983

Short-range scattering from long-range magnetic fields,
in: "Danish-Swedish analysis seminar on partial differential equations and mathematical physics", Report Series 1/1987,
with M. Loss

Some Considerations on Degenerate Control Systems: The LQR Problem.
Report Nr. 45 of SFB 003 (1995), 22pp.
with S. Thaller

Optimal Lp-Lq Estimate for the Schrödinger Semigroup with a Magnetic Field in Two Dimensions, Grazer Mathematische Berichte 328, 53-64 (1996), ISSN 1016-7692
with M. Loss

Approximation of degenerate Cauchy problems, Report Nr. 76 of SFB 003 (1996), 13pp.
with S. Thaller

Comparison Theorem for Schrödinger Semigroups with Magnetic Fields in Two Dimensions, SEAMS "International conference on Mathematics and its Applications" (1999).

Visualizing the kinematics of Dirac wave packets, preprint 2004.


Elektron-Positron Interpretation der Diracgleichung, Dissertation, Karl-Franzens Universität Graz, Juni1981

Streutheorie für die Dirac- und Schrödingergleichung mit langreichweitigen Kraftfeldern, Habilitationsschrift, Universität Graz 1987

Computer Programs

"ArgColorPlot.m", Mathematica Package, in "The InterCall Book" - Supplementary material, Trefry and Abbott (Eds), Analytica International, Perth, Australia, ISBN 0-646-35666-6, July 1998

"ColorPlot2D.m", Mathematica Package, in "The InterCall Book" - Supplementary material, Trefry and Abbott (Eds), Analytica International, Perth, Australia, ISBN 0-646-35666-6, July 1998

"ComplexPlot.m", Mathematica Package for the visualization of complex-valued functions. The Mathematica Journal, MathSource.

"VQM", Software accompanying the book "Visual Quantum Mechanics", ISBN 0-387-98929-3. European Academic Software Award 2000.

"AVQM", Software accompanying the book "Advanced Visual Quantum Mechanics", ISBN 0-387-20777-5, European Academic Software Award 2004.

"VQM packages", collection of Mathematica packages for quantum-mechanical computations and visualizations, Supplement for "VQM" and "AVQM".

"QuantumGL", with Wolfgang Thaller. Supplement for "AVQM". OpenGL-based application for 3D visualization of high-dimensional data fields.

Media Contributions

Cover image of Computers in Physics, November/December 1996

Illustrations for Quanten-Ästhetik, in Uni-Zeit 5/2000, p.4,5 und cover image

Internet-Exhibition: comart-graz. Datenstrukturen:bernd thaller: v-q-m
with Ingrid Moschik and Gerhard M Kindlinger

Internet-Exhibition: comart-graz. Datenstrukturen bernd thaller: AVQM
with Ingrid Moschik and Gerhard M Kindlinger

Visual Quantum Mechanics Examples. Contribution for the CD-ROM for the 9th Workshop on Multimedia in Physics Teaching and Learning, Graz 2004

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