Dr. Konstantin Merz Institute for Theoretical Physics Department of Physics ETH Zürich Wolfgang-Pauli-Strasse 27 8093 Zürich Switzerland Email: konstantin.merz(at)ethz.ch Office: K 22.3 Since October 2025 on leave from Institute of Analysis and Algebra, TU Braunschweig.

Research interests

• Schrödinger operators with general kinetic energies, in particular
  • eigenvalue estimates
  • heat kernel estimates
  • spectral multiplier theorems
• Functional inequalities
• Many-particle quantum systems

Open PhD position at TU Braunschweig

Publications

1. (with R. L. Frank and H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 2021 (2021), no. 3, 2284-2303 - Article - Preprint
2. (with H. Siedentop) The atomic density on the Thomas-Fermi length scale for the Chandrasekhar Hamiltonian. Rep. Math. Phys. 83 (2019), no. 3, 387-391 - Article - Preprint
3. On scales of Sobolev spaces associated to generalized Hardy operators. Math. Z. 299 (2021), no. 1, 101-121 - Article - Preprint
4. (with R. L. Frank, H. Siedentop, and B. Simon) Proof of the strong Scott conjecture for Chandrasekhar atoms. Pure Appl. Funct. Anal. 5 (2020), no. 6, 1319-1356. (issue dedicated to Yakov Sinai on his 85th Birthday) - Article - Preprint
5. (with J.-C. Cuenin) Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials. Lett. Math. Phys. 111 (2021), no. 2, paper number 46 - Article - Preprint
6. (with H. Siedentop) Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture. Ann. H. Lebesgue 5 (2022), 611-642 - Article - Preprint
7. (with R. L. Frank and H. Siedentop) Relativistic strong Scott conjecture: A short proof. In: Density Functionals for Many-Particle Systems. Mathematical Theory and Physical Applications of Effective Equations, B.-G. Englert, H. Siedentop, and M.-I. Trappe (eds.), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41, 69-79, World Scientific, Singapore, 2023 - Article - Preprint
8. On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle. J. Evol. Equ. 22 (2022), no. 3, paper number 62 - Article - Preprint
9. (with J.-C. Cuenin) Random Schrödinger operators with complex decaying potentials. Anal. PDE 18 (2025), no. 2, 279-306 - Article - Preprint
10. (with J.-C. Cuenin) On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy. In: From Complex Analysis to Operator Theory: A Panorama: In Memory of Sergey Naboko, M. Brown, F. Gesztesy, P. Kurasov, A. Laptev, B. Simon, G. Stolz, and I. Wood, Operator Theory: Advances and Applications 291, 313-340, Birkhäuser, Cham, 2023 - Article - Preprint
11. (with R. L. Frank and H. Siedentop) The Scott conjecture for large Coulomb systems: a review. Lett. Math. Phys. 113 (2023), paper number 11 - Article - Preprint
12. (with R. L. Frank) On Sobolev norms involving Hardy operators in a half-space. J. Funct. Anal. 285 (2023), no. 10, paper number 110104 - Article - Preprint
13. (with K. Bogdan) Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels. J. Math. Pures Appl. (9) 186 (2024), 176-204 - Article - Preprint
14. (with J.-C. Cuenin) Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials. To appear in RIMS Kôkyûroku Bessatsu - Preprint
15. (with K. Bogdan) Subordinated Bessel heat kernels. Theory Probab. Math. Statist. 112 (2025), 67-83 - Article - Preprint
16. (with T. A. Bui) Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space. Math. Ann. 395 (2026), paper number 28 - Artice - Preprint
17. (with K. Bogdan and T. Jakubowski) Hardy perturbations of subordinated Bessel heat kernels. Preprint
18. (with T. A. Bui and X. T. Duong) Equivalence of Sobolev norms for Kolmogorov operators with scaling-critical drift. Nonlinearity 39 (2026), no. 1, paper number 015021 - Article - Preprint
19. (with K. Bogdan) Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels. Ann. Henri Poincaré. In press - Article - Preprint
20. (with R. Frank) Sharp upper bounds for the density of relativistic atoms: Noninteracting case. To appear in Pure Appl. Funct. Anal. (issue dedicated to Barry Simonon his 80th Birthday) - Preprint
21. (with J.-C. Cuenin and E. Stefanescu) Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators. Preprint
22. (with A. Ishida) On wave operators for Hardy operators with and without perturbations. Preprint
23. (with A. Ishida) Maximal velocity estimates for Hardy operators. Preprint
24. A Hörmander spectral multiplier theorem for fractional Hardy operators. Preprint

Seminars and conferences

Minisymposium Mathematics of Complex Quantum Systems at the Joint Annual Meeting of GAMM & DMV Annual Meeting 2027 (joint with Alex Bols)

Gauss Mini Workshop on Analysis, PDE, and Mathematical Physics (23 January 2025)

GAuS online seminar (joint with Christoph Kehle and Simone Rademacher)

Minisymposium Mathematical Analysis of Complex Quantum Systems at the DMV Annual Meeting 2022 (joint with Heinz Siedentop)

Teaching / Lehre (in German)

Curriculum Vitae

Links