# Triple-Slit Experiment in the Causal Interpretation

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This Demonstration simulates the triple‐slit experiment numerically according to the causal interpretation of David Bohm and Louis de Broglie. The slits generate three Gaussian profiles in space, positioned at 0 and . The initial form of the unnormalized waves are , where are the wave numbers in the direction, are the widths of the wave packets at , are the constant phase shifts and ), are the real-valued constants with , , , and where with . In this case the total wavefunction is the superposition of the three waves , where the time evolution is to be calculated from the free Schrödinger equation (): with , and so on.

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Contributed by: Klaus von Bloh (March 2013)

After work by: Michael Schmidt and Franco Selleri

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In the program, if you increase PlotPoints, AccuracyGoal, PrecisionGoal, and MaxSteps, the results will be more accurate. The starting positions of the particles are linearly distributed around the peaks of the wave density at . Furthermore, the number of the particles depends on the initial squared amplitude of each unnormalized wave, which is proportional to , , and . If the constant phase shift of the wave from the second slit is changed, the interference pattern and therefore the motion of the particles change significantly. The particle positions are plotted against their downscaled kinetic energy along the vertical axis.

The trajectories for the double slit were first numerically calculated in [1]. The effects of empty waves are discussed in [2]. For more detailed information about Bohmian mechanics, see [3].

References

[1] C. Philippidis, C. Dewdney, and B. J. Hiley, "Quantum Interference and the Quantum Potential," *Il Nuovo Cimento B Series 11*, 52(1), 1979 pp. 15–28. doi:10.1007/BF02743566.

[2] M. Schmidt and F. Selleri, "Empty-Wave Effects on Particle Trajectories in Triple-Slit Experiments," *Foundations of Physics Letters, *4(1), 1991 pp. 1–17. doi:10.1007/BF00666413.

[3] S. Goldstein. "Bohmian Mechanics." The Stanford Encyclopedia of Philosophy. (Mar 4, 2013)plato.stanford.edu/entries/qm-bohm.

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