Article

Argaez, C and Melgaard, M (2018) Ground state solutions to Hartree–Fock equations with magnetic fields. Applicable Analysis, 97 (14). pp. 2377-2403. ISSN 0003-6811

Guo, Zhenyu, Melgaard, Michael and Zou, Wenming (2017) Schrödinger equations with magnetic fields and Hardy-Sobolev critical exponents. Electronic Journal of Differential Equations, 2017 (199). pp. 1-18. ISSN 1072-6691

Kungsman, J and Melgaard, Michael (2017) Poisson wave trace formula for perturbed Dirac operators. Journal of Operator Theory, 77 (1). pp. 133-147. ISSN 1841-7744

Argaez, C and Melgaard, M (2016) Minimizers for open-shell, spin-polarised Kohn–Sham equations for non-relativistic and quasi-relativistic molecular systems. Methods and Applications of Analysis, 23 (3). pp. 269-292. ISSN 1073-2772

Kungsman, J and Melgaard, M (2014) Existence of Dirac resonances in the semi-classical limit. Dynamics of Partial Differential Equations, 11 (4). pp. 381-395. ISSN 1548-159X

Kungsman, J and Melgaard, M (2014) Complex absorbing potential method for the perturbed Dirac operator. Communications in Partial Differential Equations, 39 (8). pp. 1451-1478. ISSN 0360-5302

Kungsman, J and Melgaard, M (2014) Complex absorbing potential method for Dirac operators. Clusters of resonances. Journal of Operator Theory, 71 (1). pp. 259-283. ISSN 1841-7744

Kungsman, J and Melgaard, M (2014) Existence of Dirac resonances in the semi-classical limit. Dynamics of Partial Differential Equations, 11 (4). pp. 381-395. ISSN 1548159X

Enstedt, M and Melgaard, M (2012) Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. Journal of Differential Equations, 253 (6). pp. 1729-1743. ISSN 0022-0396

Chiumiento, Eduardo and Melgaard, Michael (2012) Stiefel and Grassmann manifolds in quantum chemistry. Journal of Geometry and Physics, 62 (8). pp. 1866-1881. ISSN 0393-0440

Melgaard, M and Zongo, F (2012) Multiple solutions of the quasi-relativistic Choquard equation. Journal of Mathematical Physics, 53. 033709. ISSN 0022-2488

Argaez, Carlos and Melgaard, Michael (2012) Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry. Nonlinear Analysis: Theory, Methods and Applications, 75 (1). pp. 384-404. ISSN 0362-546X

Argaez, Carlos and Melgaard, Michael (2012) Existence of a minimizer for the quasi-relativistic Kohn-Sham model. Electronic Journal of Differential Equations, 2012 (18). pp. 1-20. ISSN 1072-6691

Melgaard, M and Zongo, F (2012) Multiple solutions of the quasi relativistic Choquard equation. Journal of Mathematical Physics, 53. 033709. ISSN 0022-2488

Kungsman, Jimmy and Melgaard, Michael (2010) Complex absorbing potential method for systems. Dissertationes Mathematicae, 469. pp. 1-58. ISSN 0012-3862

Enstedt, M and Melgaard, M (2009) Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations. International Journal of Mathematics and Mathematical Sciences, 2009. pp. 1-20. ISSN 0161-1712

Enstedt, M and Melgaard, M (2008) Existence of a solution to Hartree-Fock equations with decreasing magnetic field. Nonlinear Analysis: Theory, Methods and Applications, 69 (7). pp. 2125-2141. ISSN 0362-546X

Enstedt, Mattias and Melgaard, Michael (2008) Non-existence of a minimizer to the magnetic Hartree-Fock functional. Positivity, 12 (4). pp. 653-666. ISSN 1385-1292

Melgaard, Michael (2007) Scattering properties for a pair of Schrödinger type operators on cylindrical domains. Central European Journal of Mathematics, 5 (1). pp. 134-153. ISSN 1895-1074

Melgaard, M (2007) Confinement effects on scattering for a nanoparticle. Acta Physica Polonica B, 38 (1). pp. 197-214. ISSN 0587-4254

Melgaard, Michael (2007) Quantum collisions in semi-constrainted structures. Modern Physics Letters B, 21 (13). pp. 767-779. ISSN 0217-9849

Melgaard, Michael (2006) Thresholds properties for matrix-valued Schr\"{o}dinger operators, II. Resonances. Journal of Differential Equations, 226 (2). pp. 687-703. ISSN 0022-0396

Johnson, Tomas and Melgaard, Michael (2005) On the maximal ionization for the atomic Pauli operator. Proceedings of the Royal Society A, 461 (2063). pp. 3355-3364. ISSN 1471-2946

Melgaard, Michael (2005) Optimal limiting absorption principle for a Schrödinger type operator on a Lipschitz cylinder. Manuscripta Mathematica, 118 (2). pp. 253-270. ISSN 0025-2611

Melgaard, Michael (2005) Thresholds properties for matrix-valued Schrödinger operators. Journal of Mathematical Physics, 46 (8). 083507. ISSN 0022-2488

Brasche, Johannes F and Melgaard, Michael (2005) The Friedrichs extension of the Aharonov-Bohm Hamiltonian on a disk. Integral Equations and Operator Theory, 52 (3). pp. 419-436. ISSN 0378-620X

Melgaard, Michael (2004) Bound states for the three-dimensional Aharonov-Bohm quantum wire. Few-Body Systems, 35 (1-2). pp. 77-97. ISSN 0177-7963

Melgaard, M, Ouhabaz, E-M and Rozenblum, G (2004) Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians. Annales Henri Poincare, 5 (5). pp. 979-1012. ISSN 1424-0637

Melgaard, Michael (2003) Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field. Central European Journal of Mathematics, 1 (4). pp. 477-509. ISSN 1895-1074

Melgaard, M and Rozenblum, G (2003) Eigenvalue asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic fields of full rank. Communications in Partial Differential Equations, 28 (3-4). pp. 697-736. ISSN 0360-5302

Melgaard, Michael (2002) On bound states for systems of weakly coupled Schrödinger equations in one space dimension. Journal of Mathematical Physics, 43 (11). pp. 5365-5385. ISSN 0022-2488

Melgaard, Michael (2002) New approach to quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field. Few-Body Systems, 32 (1-2). pp. 1-22. ISSN 0177-7963

Melgaard, Michael (2002) Spectral properties in the low-energy limit of one-dimensional Schrödinger operators H = –d2/dx2 + V. The Case 〈1, V1〉 ≠ 0. Mathematische Nachrichten, 238 (1). pp. 113-143. ISSN 0025-584X

Jensen, A and Melgaard, M (2002) Perturbation of eigenvalues embedded at a threshold. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 132 (1). pp. 163-179. ISSN 0308-2105

Melgaard, Michael (2001) Spectral properties at a threshold for two-channel Hamiltonians. II. Applications to scattering theory. Journal of Mathematical Analysis and Applications, 256 (2). pp. 568-586. ISSN 0022-247X

Melgaard, Michael (2001) Spectral properties at a threshold for two-channel Hamiltonians I. Abstract theory. Journal of Mathematical Analysis and Applications, 256 (1). pp. 281-303. ISSN 0022-247X

Melgaard, Michael and Rozenblum, Gregory V (1996) Spectral estimates for magnetic operators. Mathematica Scandinavica, 79. pp. 237-254. ISSN 0025-5521

Book Section

Rozenblum, G and Melgaard, M (2005) Schrödinger operators with singular potentials. In: Chipot, M and Quittner, P (eds.) Handbook of differential equations : stationary partial differential equation. Handbook of differential equations, 2 . Elsevier/North-Holland, Amsterdam, pp. 407-517. ISBN 9780444520456

Conference or Workshop Item

Melgaard, Michael (2007) Confinement effects on scattering for a nanoparticle. In: Proceedings of the International Conference ``APLIMAT 2007'', February 6 - 9, 2007, Bratislava, Slovak Republic.

Melgaard, Michael (2006) Strong asymptotic completeness of a quantum wire. In: Proceedings of the International Conference ``Days on Diffraction 2006'', May 30 -- June 2, 2006, St. Petersburg, Russia.