A novel approach to Bohmian mechanics using an uncompressed particle method

Abstract We propose extending Bohmian mechanics (BM) with the moving particle semi-implicit method, a particle method for uncompressed fluids. The application of this method prevents the node of the Bohm quantum potential from breaking numerical calculations while maintaining a low calculation cost. We validated our extended method by comparing our results with those from the conventional method for a one-dimensional harmonic oscillator, Gaussian barrier and rectangular barrier. The proposed method was found to simulate the temporal changes in the probability density for a rectangular barrier. In addition, the relational equation obtained by this method reveals an interesting correspondence between the pressure of a classical fluid and the Bohm quantum potential.