Constructing Numerical Methods For Solving The Guiding Equation In Bohmian Mechanics

Sammanfattning: The aim of this thesis was to simulate a part of a proposed experiment by Lev Vaidman by using Bohmian mechanics. To do this a numerical method for solving the Schrödinger equation and theguiding equation was created, with several ways of making the simulation more efficient.To make the simulation work more efficiently the Schrödinger equation was applied to only a small region of the whole setup. This region followed the wavefunction of significant values and could change size during the simulation. A beam splitter was constructed in the form of a thin potential barrier. The beam splitter was tested to verify that the reflected and transmitted angles agreed with expectations. A virtual detector was constructed and used for the calibration of the beam splitter to determine which potential resulted in dividing the wave packet into two wave packets of equal intensity. A fixed angle mirror was used for testing the reflection of a wave packet for the reflected angle and concluded that it agreed with the expectations for it. Testing a time dependent mirror for different frequencies and amplitudes was performed, with the result that the numerical method could be used to determine the particles’ trajectories. These results were used to construct a larger setup that was a small part of Vaidman’s proposed experiment. These setups were done in several version. All setups had one wave packet that went through one beam splitter and separated into two wave packets. These two wave packets reflected at two mirrors with different frequencies and then interfered with each other at either free space or at another beam splitter. The result of the simulation of these setups was that the particles’ trajectories could be calculated with the guiding equation.