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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Gittertheorien und Spinmodelle

MP 5.5: Vortrag

Dienstag, 19. März 2019, 15:50–16:10, HS 23

Hamilton's equations of motion for quantum systems — •Michael Beyer¹, Jeanette Köppe², Markus Patzold¹, and Wolfgang Paul¹ — ¹Martin-Luther-Universität Halle-Wittenberg — ²Westfälische Wilhelms-Universität Münster

Quantum systems can be described in terms of kinematic and dynamic equations within the stochastic picture of quantum mechanics where the particles follow some conservative diffusion process. We show that the reformulation of the quantum Hamilton principle as a stochastic optimal control problem allows us to derive these quantum Hamilton equations of motion for multidimensional systems which can be seen as a generalization of Hamilton's equations of motion to the quantum world. Due to their similar structure it is possible to draw analogies to classical mechanics where one encounters some similarities for quantum systems, e.g. the decoupling of the center-of-mass motion in multi-particle systems or the Kepler problem as the special case of the two-body problem where we present numerical results for the hydrogen atom.