Corresponding Member of the Division of Mathematics and the Natural Sciences abroad since 1990
- Mathematics Department, California Institute of Technology
- Mathematical physics
- Complex analysis
- American Academy of Arts and Sciences
- American Mathematical Society
- American Physical Society
- Henri Poincare Prize
- Stampacchia Prize
- D. Sc. h. c., Technion-Israel Institute of Technology
- Honorary Fellow, University of Wales Swansea
- D. h. c. Ludwig-Maximilians-Universität München
- Killip, R.; Simon, B. (2003) Sum rules for Jacobi matrices and their applications to spectral theory. Annals of Mathematics, Bd. 158, S. 253-321.
- Simon, B.; Lieb, E. (1977) The Thomas-Fermi theory of atoms, molecules and solids. Advances in Mathematics, Bd. 23, S. 22-116.
- Simon, B.; Fröhlich, J.; Spencer, T. (1976) Infrared bounds, phase transitions and continuous symmetry breaking. Communications in Mathematical Physics, Bd. 50, S. 79-85.
- Simon, B.; Lieb, E. (1973) Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Annals of Mathematics, Bd. 97, S. 247-274.
- Reed, M.; Simon, B. (1972) Methods of Modern Mathematical Physics, Vol. 1.1972 - 4.1979.; San Diego, Calif.: Academic Press.