Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Statistical Physics II (General)

DY 25.11: Talk

Tuesday, March 13, 2018, 12:45–13:00, BH-N 243

Excited States in Nelson's Stochastic Mechanics — •Markus Patzold¹, Jeanette Köppe¹, Michael Beyer¹, Wilfried Grecksch², and Wolfgang Paul¹ — ¹Martin Luther Universität Halle-Wittenberg, Institut für Physik — ²Martin Luther Universität Halle-Wittenberg, Institut für Mathematik

In 1966 Edward Nelson successfully derived the Schrödinger equation for non-relativistic spinless particles in the ground state using stochastic differential equations (FBSDE). Solutions of the Schrödinger equation can be used to generate particle paths in this context. Pavon generalized his ideas 1995 to the quantum Hamilton principle, similar to the classical one, introducing a stochastic variational principle. Furthermore, a stochastic optimal control approach is equivalent to the above mentioned one and can be solved without the Schrödinger equation as it was shown by Köppe, et al. in 2017.

However, these equations lead to the ground state of the system only. In the talk I will show how to bypass this problem, adapting the stochastic equations, by exploiting the concept of supersymmetry (SUSY) to give iterative equations for all excited states in arbitary dimensions. Numerical calculations for the double well and hydrogen problem as well as analytical calculations for the harmonic oscillator in d dimensions and the radial hydrogen part including a symmetry analysis will be discussed.