Probability Current Density or Flux

[manofphysics]

Normally, when we encounter un normalizable wave functions, they are considered to be representing streams of particles.Like in the case of of transmission thru a step potential,We find out the probability flux of reflected wave and transmitted wave and hence find transmission coeff.
Can anyone explain this to me physically? like what is probability flux physically ( I am familiar with the mathematics of it, I want the physical significance)and what is the meaning/significance of transmission coeff. and where do streams of particles come in here?

 

[manofphysics]

Anybody?

 

[Matterwave]

Probabilities are probabilities, I don't see how they are "physical" in any sense. The transmission coefficient is just the probability that a particle incident on the potential will pass through that potential. A probability current density (or flux as you say) is not physical either. It's just saying the probability of where the particle is are changing, and the flux just tells us how those probabilities are changing.

But to clear up something, the wave functions are perfectly normalizable, we can form wave packets just like with the free particle no problem; however, doing transmission and reflection on wave packets is a huge pain in the neck, so we usually just use the unnormalized wave functions to do the analysis. It turns out, the difference between using wave packets and our regular wave functions isn't very significant (at least, not for students).

 

[Demystifier]

Normally, when we encounter un normalizable wave functions, they are considered to be representing streams of particles.Like in the case of of transmission thru a step potential,We find out the probability flux of reflected wave and transmitted wave and hence find transmission coeff.
Can anyone explain this to me physically? like what is probability flux physically ( I am familiar with the mathematics of it, I want the physical significance)and what is the meaning/significance of transmission coeff. and where do streams of particles come in here?

Probability flux has a physical meaning within (and perhaps only within) the Bohmian interpretation. In this interpretation, particles of an statistical ensemble move with a velocity proportional to the probability current.