Rostock 2019 – wissenschaftliches Programm

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MO: Fachverband Molekülphysik

MO 10: Posters 1: Cold Molecules, High Resolution Spectroscopy, and Theory

MO 10.20: Poster

Dienstag, 12. März 2019, 16:30–18:30, S Foyer LLM

Comparison of two different ways to calculate expectation values — •Klaus Renziehausen and Ingo Barth — Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Saale), Germany

We analyze two different ways to calculate quantum mechanical expectation values for several observables. The first ansatz is just the direct calculation of the quantum mechanical expectation value, the second ansatz is to calculate this expectation value using the Ehrenfest theorem. We have performed those calculations for the temporal mass change, the momentum, the force, the torque, and the angular velocity of a particle in three dimensions. As a result, we found for each of these observables an integral equation. On one side of this equation an integrand depending on the mass density appears, while we find on the other side an integrand depending on the mass current density. So, we can calculate these expectation values either using the mass density or the mass current density (as an exception the analysis for the expectation value of the azimuth angular velocity is more complicated). This has application possibilities for molecular systems where electronic current densities cannot be calculated within the Born-Oppenheimer approximation. The papers [I. Barth et al., Chem. Phys. Lett. 481, 118-123 (2009)] and [T. Schaupp, J. Albert, V. Engel, Eur. Phys. J. B 91, 97 (2018)] can be interpreted as examples for such applications.