# Bohm Trajectories for Quantum Particles in a Uniform Gravitational Field

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This Demonstration studies a free-falling quantum particle with mass in a uniform gravitational potential (in the Earth's gravitational field: ). The equations of motion can be solved analytically for the classical and quantum-mechanical case. For the classical (i.e., Newtonian) case, the force is , which leads to the kinematic equation of motion: with constant acceleration , constant initial velocity , and initial position . Classically, the kinematic equation is independent of the mass, which shows that all bodies with different masses fall with an equal acceleration . In the quantum case the time-evolution of the wavefunction for an initial Gaussian packet (initial maximum , group velocity , initial density , mass ) in a uniform field with the strength is described by a complex-valued field:

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Contributed by: Klaus von Bloh (March 2011)

Open content licensed under CC BY-NC-SA

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Reference

[1] P. Holland, *The Quantum Theory of Motion*, Cambridge: Cambridge University Press, 1993.

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