Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Statistical Physics II (General)

DY 25.10: Talk

Tuesday, March 13, 2018, 12:30–12:45, BH-N 243

Quantum Hamilton equations for multidimensional problems — •Michael Beyer¹, Jeanette Köppe¹, Markus Patzold¹, Wilfried Grecksch², and Wolfgang Paul¹ — ¹Institute for physics, Martin-Luther-Universität Halle-Wittenberg — ²Institute for mathematics, Martin-Luther-Universität Halle-Wittenberg

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 Newton's equations of motion to the quantum world. In analogy to classical mechanics 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.