Berlin 2024 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Poster (joint session MP/QI)

MP 7.1: Poster

Tuesday, March 19, 2024, 11:00–13:00, Poster B

Machine Learning Quantum Mechanical Ground States based on Stochastic Mechanics — •Kai-Hendrik Henk and Wolfgang Paul — Martin-Luther-University, Halle(Saale), Germany

The Rayleigh-Ritz variation principle is a proven way to find ground states and energies for bound quantum systems in the Schrödinger picture. Advances in machine learning and neural networks make it possible to extend it from an analytical search from a subspace of the complete Hilbert space to the a numerical search in the almost complete Hilbert space. In this paper, we extend the Rayleigh-Ritz principle to Nelson’s stochastic mechanics formulation of non-relativistic quantum mechanics, and propose a new algorithm to find the osmotic velocities u(x), which contain the information of a quantum systems in this picture. As a proof of concept, we calculated u(x) for one dimensional systems, the harmonic oscillator, the double well and the Pöschl-Teller potential. To obtain exited states, we calculate ground states of super symmetrical partner Hamiltonians for each of these potentials. We will show that this method is more efficient than the stochastic optimal control algorithm, that was the usual method to obtain osmotic velocities without going back to the Schrödinger equation.

Keywords: Machine Learning; Genetic Algorithms; Neural Networks; Stochastic Quantum Mechanics; Rayleigh-Ritz Variational Principle