References
- Szabo A, Ostlund NS. Modern quantum chemistry: an introduction to advanced electronic structure theory. New York (NY): MacMillan; 1982.
- Fröhlich J, Lieb EH, Loss M. Stability of Coulomb systems with magnetic fields. I. The one-electron atom. Commun Math Phys. 1986;104(2):251–270.
- Lieb EH, Loss M, Solovej JP. Stability of matter in magnetic fields. Phys Rev Lett. 1995;75(6):985–989.
- Loss M, Yau HT. Stability of Coulomb systems with magnetic fields. III. Zero energy bound states of the Pauli operator. Commun Math Phys. 1986;104:283–290.
- Balinsky AA, Evans WD. On the zero modes of Pauli operators. J Funct Anal. 2001;179(1):120–135.
- Lieb EH, Simon B. The Hartree-Fock theory for Coulomb systems. Commun Math Phys. 1977;53(3):185–194.
- Enstedt M, Melgaard M. Existence of a solution to Hartree-Fock equations with decreasing magnetic fields. Nonlinear Anal. 2008;69(7):2125–2141.
- Solovej JP. Proof of the ionization conjecture in a reduced Hartree-Fock model. Invent Math. 1991;104(2):291–311.
- Esteban MJ, Lions P-L. Stationary solutions of nonlinear Schrödinger equations with an external magnetic field. In: Partial differential equations and the calculus of variations. Vol. I, Progress in nonlinear differential equations and their applications. Boston (MA): Birkhäuser; 1989. p. 401–449.
- Lions P-L. Solutions of Hartree-Fock equations for Coulomb systems. Commun Math Phys. 1987;109(1):33–97.
- Kato T. Remarks on Schrödinger operators with vector potentials. Integr Equ Oper Theory. 1978;1(1):103–113.
- Simon B. Maximal and minimal Schrödinger forms. J Oper Theory. 1979;1(1):37–47.
- Lieb EH, Loss M. Analysis. 1st ed. Providence (RI): American Mathematical Society; 1997.
- Edmunds DE, Evans WD. Spectral theory and differential operators. New York (NY): Clarendon Press, Oxford University Press; 1987.
- Kato T. Perturbation theory for linear operators. Reprint of the 1980 edition. Classics in mathematics. Berlin: Springer-Verlag; 1995.
- Avron J, Herbst I, Simon B. Schrödinger operators with magnetic fields: I. General interactions. Duke Math J. 1978;45:847–883.
- Lieb EH. Variational principle for many-fermion systems. Phys Rev Lett. 1981;46(7):457–459. Erratum, Phys Rev Lett. 1981;47(1):69.
- Lieb EH, Thirring W. Bound for the kinetic energy of fermions which proves the stability of matter. Phys Rev Lett. 1975;35:687–689. Errata ibid. 1975;35:1116.
- Melgaard M, Rozenblum G. Schrödinger operators with singular potentials. In: Chipot M, Quittner P, editors. Stationary partial differential equations. Vol. II, Handbook of differential equations. Amsterdam: Elsevier/North-Holland; 2005. p. 407–517.
- Kato T. Fundamental properties of Hamiltonian operators of Schrödinger type. Trans Amer Math Soc. 1951;70:195–211.
- Leinfelder H. Gauge invariance of Schrödinger operators and related spectral properties. J Oper Theory. 1983;9(1):163–179.
- Bach V. Error bound for the Hartree-Fock energy of atoms and molecules. Commun Math Phys. 1992;147(3):527–548.
- Barbaroux J-M, Farkas W, Helffer B, et al . On the Hartree-Fock equations of the electron-positron field. Commun Math Phys. 2005;255(1):131–159.
- Coleman AJ. Structure of fermion density matrices. Rev Mod Phys. 1963;35:668–689.
- Gontier D. Existence of minimizers for Kohn-Sham within the local spin density approximation. Nonlinearity. 2015;28(1):57–76.