Editing De Broglie–Bohm theory (section)

=== Quantum trajectory method ===
Work by [[Robert E. Wyatt]] in the early 2000s attempted to use the Bohm "particles" as an adaptive mesh that follows the actual trajectory of a quantum state in time and space. In the "quantum trajectory" method, one samples the quantum wavefunction with a mesh of quadrature points. One then evolves the quadrature points in time according to the Bohm equations of motion. At each time step, one then re-synthesizes the wavefunction from the points, recomputes the quantum forces, and continues the calculation. (QuickTime movies of this for H + H<sub>2</sub> reactive scattering can be found on the [http://research.cm.utexas.edu/rwyatt/movies/qtm/index.html Wyatt group web-site] at UT Austin.)
This approach has been adapted, extended, and used by a number of researchers in the chemical physics community as a way to compute semi-classical and quasi-classical molecular dynamics. A 2007 issue of [[The Journal of Physical Chemistry A]] was dedicated to Prof. Wyatt and his work on "computational Bohmian dynamics".<ref>{{cite journal |last1= Wyatt |first1= Robert |date= 11 Oct 2007 |title= The Short Story of My Life and My Career in Quantum Propagation |url= https://pubs.acs.org/doi/full/10.1021/jp079540%2B  |journal= The Journal of Physical Chemistry A |volume= 111 |issue= 41 |pages= 10171–10185 |doi= 10.1021/jp079540+ |pmid= 17927265 |bibcode= 2007JPCA..11110171. |access-date= 2023-03-18}}</ref>

[[Eric R. Bittner]]'s group<ref name="h523">{{cite web | title=Bittner Group Webpage | website=k2.chem.uh.edu | date=2021-03-10 | url=http://k2.chem.uh.edu/ | archive-url=http://web.archive.org/web/20210805161220/http://k2.chem.uh.edu/ | archive-date=2021-08-05 | url-status=dead | access-date=2024-07-10}}</ref> at the [[University of Houston]] has advanced a statistical variant of this approach that uses Bayesian sampling technique to sample the quantum density and compute the quantum potential on a structureless mesh of points. This technique was recently used to estimate quantum effects in the heat capacity of small clusters Ne<sub>n</sub> for ''n'' ≈ 100.

There remain difficulties using the Bohmian approach, mostly associated with the formation of singularities in the quantum potential due to nodes in the quantum wavefunction. In general, nodes forming due to interference effects lead to the case where <math>R^{-1}\nabla^2R \to \infty.</math> This results in an infinite force on the sample particles forcing them to move away from the node and often crossing the path of other sample points (which violates single-valuedness). Various schemes have been developed to overcome this; however, no general solution has yet emerged.

These methods, as does Bohm's Hamilton–Jacobi formulation, do not apply to situations in which the full dynamics of spin need to be taken into account.

The properties of trajectories in the de Broglie–Bohm theory differ significantly from the [[method of quantum characteristics|Moyal quantum trajectories]] as well as the [[Quantum stochastic calculus#Quantum trajectories|quantum trajectories]] from the unraveling of an open quantum system.