From atoms to crystals: a mathematical journey. (English) Zbl 1136.81371
Summary: We present an overview of some works on the models of computational quantum chemistry. We examine issues such as the existence of ground states (both for the electronic structure and the configuration of nuclei), the foundations of the models of the crystalline phase, and the macroscopic limits. We emphasize the connections between the physical modelling, the numerical concerns and the mathematical analysis of the problems.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 35B35 | Stability in context of PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35J60 | Nonlinear elliptic equations |
| 35Q40 | PDEs in connection with quantum mechanics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81V55 | Molecular physics |
| 82D25 | Statistical mechanics of crystals |
Software:
CRYSTALReferences:
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