ATOMIC and MOLECULAR PHYSICS

test items (plan)

PHYSICS MSc – 2018 autumn semester

 

1) Introduction: Rydberg-constant, separating the center of mass motion in the two-body problem, atomic units, virial theorem, the role of Ekin and Epot in the formation of a chemical bond on the example of the H2+ molecular ion

 

2) Principles 1: the necessity of approximations, perturbational vs. variational methods, the variation principle, Eckart’s inequality, nonlinear variation (two examples: H-exp, H-gauss),

 

3) Principles 2: linear variation, Löwdin’s orthogonalization, Born--Oppenheimer approximation, Hellmann--Feynman theorem

 

4) He atom 1: ground state, screening, Cb-integral, comparison of various approximations,

Hartree-Fock method for the ground state of He, Hylleraas-solution, Pekeris-solution, various types of correlation

 

5) He atom 2: excited states, exchange integral (a paper for K>0 ), ortho-He, para-He, two-electron Slater determinants, Fermi-hole, Coulomb-hole

 

6) Dirac-equation: Application of the Dirac-equation for H atom, the spin in electric and/or magnetic field, the spin-orbit coupling     (hand written formulas and proofs)

 

7) Hund’s rules: atomic term symbols, LS-coupling, jj-coupling, the role of configurational interaction on the example of Mg atom, periodic system, Grotrian diagram

 

8) H2+ molecular ion: description with various approximate (and exact) methods, molecular orbitals, LCAO method

 

9) H2 molecule:  description with various approximate methods, comparison of the MO and VB methods

 

10) Diatomic molecules: correlation diagram, avoided crossing, N2 and O2 molecule, paramagnetism of the latter

 

11) Polyatomic molecules 1: energy levels and vibrational modes of H2O molecule, hybridisation

 

12) Polyatomic molecules 2: the role of symmetries, the use of character tables (NH3, CH4, C60) 

 

 

Budapest, 2018-09-21.                                                 Kürti Jenő


 

Recommended literature:

- P. Atkins, R. Friedman: Molecular Quantum Mechanics, Oxford University Press 2010

- I. Mayer: Simple Theorems, Proofs, and Derivations in Quantum Chemistry, Springer Science+Business Media New York 2003

- H. Haken, H.C. Wolf: Molecular Physics and Elements of Quantum Chemistry, Springer-Verlag Berlin Heidelberg 1987

- H. Haken, H.C. Wolf: Molekülphysik und Quantenchemie, Springer-Verlag Berlin Heidelberg 1995

- The Feynman Lectures in Physics: http://www.feynmanlectures.info/

 

- Kapuy Ede, Török Ferenc, Az atomok és molekulák kvantumelmélete

- Marx György: Kvantummechanika

- Erostyák János -- Kürti Jenő -- Raics Péter -- Sükösd Csaba: Fizika III. egyetemi tankönyv megfelelő fejezetei 


 

Last updated on 21st September 2018 by Jenő Kürti