Year: 2010
Type: preprint
Abstract: A solution $ψ$ to Schrödinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\hbar \Im \left( \bigtriangledown ψ/mψ\right) .$ In the case of one specific non-differentiable weak solution $Ψ$ we show how Bohmian trajectories can be obtained for $Ψ$ from the trajectories of a sequence $Ψ_{n}\rightarrow Ψ.$ (For any real $t$ the sequence $Ψ_{n}\left( t,\cdot \right) $ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectors $Ψ$ in the Hilbert space on which the Schrödinger evolution $% Ψ\mapsto e^{-iht}Ψ$ acts.
Source: arXiv (Cornell University)
Authors: Gruebl, Gebhard, Penz, Markus
Institution: Universität Innsbruck
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300670862