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Last update: T_KFES (15.05.2014)
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Last update: Mgr. Jindřich Kolorenč, Ph.D. (29.04.2019)
1. A. Szabo, N. S. Ostlund, Modern quantum chemistry, Dover Publications, 1996 2. G. F. Giuliani, G. Vignale, Quantum theory of the electron liquid, Cambridge Univer- sity Press, 2005 3. E. A. Hylleraas, Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium, Z. Physik 54, 347-366 (1929); anglický pre- klad je soucástí H. Hettema, Quantum chemistry: Classic scientic papers, World Scientic, 2000 4. B. L. Hammond, W. A. Lester, jr., P. J. Reynolds, Monte Carlo methods in ab initio quantum chemistry, World Scientic, 1994 5. I. Kosztin, B. Faber, K. Schulten, Introduction to the diffusion Monte Carlo method, Am. J. Phys. 64, 633-644 (1996) 6. J. Kolorenc, L. Mitas, Applications of quantum Monte Carlo methods in condensed systems, Rep. Prog. Phys. 74, 026502 (2011) 3 |
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Last update: Mgr. Jindřich Kolorenč, Ph.D. (29.04.2019)
1. Hartree-Fock approximation: elementary properties and weaknesses, preference of magnetically ordered states, spin contamination; illustrations on the hyd- rogen molecule and homogeneous phases of the electron gas; Overhauser’s theorem (optional) 2. helium atom and helium-like ions: analytical properties of the many-body wave functions in Coulomb systems, Hylleraas’ variational method (or how to hold together the negative hydrogen ion with just a pen and paper), amount of correlations in orthohelium and parahelium 3. variational Monte Carlo: Jastrowcorrelation factor, evaluation of quantum-mecha- nical expectation values by means of stochastic integration, Metropolis algori- thm for generation of random numbers with complicated multivariate distri- butions, elementary properties of Markov chains (that represent the basis of the Metropolis algorithm) 4. diffusion Monte Carlo: projection of the exact ground state from an approximate solution, Feynman-Kac formula, stochastic evaluation of the path integral, fermion sign problem, examples of applications 2 |