The discussion centers on the concept of probability current density in quantum mechanics (QM), particularly its role in the continuity equation. While traditional interpretations like the Copenhagen interpretation lack a physical interpretation for probability current, the Bohmian interpretation (BI) provides clarity by associating particle trajectories with the probability current. In BI, the velocity of a particle is directly proportional to the probability current at its location, ensuring that the statistical distribution of particle positions aligns with the square of the wave function's amplitude, |psi|^2.
PREREQUISITESStudents and researchers in quantum mechanics, physicists exploring interpretations of quantum theory, and anyone seeking to understand the implications of probability current density in quantum systems.
Even though the probability current is mentioned in many textbooks on QM, it does not have any physical interpretation within the conventional "Copenhagen" interpretation of QM. Yet, it does play a physical role in some alternative interpretations such as the Bohmian interpretation (BI). In BI, particles have deterministic trajectories and the velocity of the particle at a given point is proportional to the value of the probability current at that point. If you consider a statistical ensemble of many such trajectories, the continuity equation explains why such trajectories are compatible with the fact that probability density of particle positions is proportional to |psi|^2. For some non-technical aspects of BI see e.g.mess1n said:I'm going over the continuity equation and I'm having some problems getting an intuitive grasp of probability current density. I can't get an idea of what it is. I know the equation, but I don't really know what it means. Could anyone help me out?
Cheers,
Andrew