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
Probability current density is a concept in quantum mechanics that describes the flow of probability associated with a quantum particle. It is a vector field that represents the rate of change of the probability density of a particle at a given point in space.
Probability current density is directly related to probability density, as it represents the flow of probability in a particular direction. The magnitude of the probability current density at a given point is proportional to the probability density at that point.
The magnitude and direction of probability current density are affected by several factors, including the wavefunction of the particle, the potential energy of the system, and the presence of magnetic and electric fields.
Probability current density is typically measured using mathematical equations and calculations based on the wavefunction of the particle. It can also be visualized and studied through the use of quantum mechanical simulations and experiments.
Probability current density is a fundamental concept in quantum mechanics that helps us understand the behavior and motion of quantum particles. It allows us to make predictions about the movement and interactions of particles in a quantum system, and is essential for studying and developing technologies such as quantum computing.