A free electron, or any other quantum particle, has an uncertain position/momentum, according to Heisenberg uncertainty principle. The squared amplitude of the wavefunction determines the probability of finding the electron at any point of the space. Accordingly, atomic orbitals are attributed certain shapes (like spherical), within which this probability is higher, but they give no information about the exact position of the electron.

However, in the Bohmian interpretation, there is no such thing as inherent uncertainty, i.e. the uncertainty is just because we can't measure the position of the particle without disturbing its wavefunction. In other words, the particle does have a certain position and trajectory, on which it's moving as determined by the wavefunction (guiding wave).

My question is, if the particle (say a free electron, or any electron in an atom) is moving on a certain trajectory in this interpretation, then what is that trajectory like? Is it supposed to have a certain shape, or it may have any random shape, depending on what the pilot wave is?

P.S. Most of the pictures in papers and scientific websites show the trajectories in a double-slit experiment (see the last picture here: http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/whatisbm_pictures_doubleslit.html). These trajectories look very ordered and well-shaped, but does any particle have such ordered trajectories?


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