Differential Equations of Quantum Mechanics

Abstract

We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems. Contents 1. Preface 1 Acknowledgments 2 2. Schrödinger equation 2 3. Including photons (Nonrelativistic QED) 4 4. Effective Equations 6 5. Hartree-Fock-Bogolubov system 8 6. Bogolubov-de Gennes system 9 7. Ginzburg-Landau equations 12 8. Summary 14 9. Remarks on literature 15 Appendix A. The NR QED Hamiltonian 17 Appendix B. Hartree-Fock-Bogolubov equations 18 Appendix C. Bogolubov-de Gennes Equations: Discussion 19 References 20 1 ONEPAS and MCQM stand for Online Northeast PDE and Analysis Seminar and Mathematical Challenges in Quantum Mechanics.