Probability current versus electric current

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Discussion Overview

The discussion revolves around the relationship between probability current and electric current in quantum mechanics. Participants explore whether these two concepts are fundamentally the same or different, considering their definitions and physical implications.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions if probability current and electric current are the same, noting that both obey the continuity equation.
  • Another participant asserts that they are different, emphasizing that boundary conditions apply to electric current but not to probability current, and that their physical significance differs.
  • A later reply suggests that probability current can exist in electrically neutral bodies, reinforcing the distinction between the two currents.
  • Another participant challenges this by asking if electric current can also exist in electrically neutral bodies.
  • One participant clarifies that probability current can arise in quantum mechanics involving uncharged particles like neutrons or neutrinos.
  • In contrast, a different participant argues that, apart from coupling constants, probability current and electric current are essentially the same, citing historical context and formal proofs in quantum mechanics that support this view.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between probability current and electric current, with no consensus reached. Some argue for their equivalence under certain conditions, while others maintain they are fundamentally different.

Contextual Notes

Participants highlight various assumptions regarding boundary conditions and the nature of the particles involved, which may influence the interpretation of the currents. The discussion also touches on the implications of symmetries and conservation laws in quantum mechanics.

BeauGeste
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are these different quantum mechanically?

I thought they were the same since probability current density obeys the continuity equation as the electric current density must also.

prob. current density: ~ psi* grad psi - psi grad psi*
electric current density ~ <psi| p |psi>

are they the same?
 
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They are different, boundary condition is required in the latter case.
The latter case is not dependent on position, while the former is dependent on position.
They are different in the physical significance.
 
Last edited:
thanks. that helps.
 
You could have a probability current when dealing with an electrically neutral body. So, no, they're not really the same thing.
 
Parlyne said:
You could have a probability current when dealing with an electrically neutral body. So, no, they're not really the same thing.

Huh? Can't you also have an electric current in an electrically neutral body?
 
I meant to say you can have a probability current when doing quantum mechanics with uncharged objects like neutrons or neutrinos.
 
BeauGeste said:
are these different quantum mechanically?

I thought they were the same since probability current density obeys the continuity equation as the electric current density must also.

prob. current density: ~ psi* grad psi - psi grad psi*
electric current density ~ <psi| p |psi>

are they the same?



Yes, or course they are, apart from coupling constants. It's an old idea -- say for a problem concerning ionization of a gas illuminated by strong radiation. It's basic to QM, in particular, to suppose that a charged particle with mass and charge will have identical distributions for mass and charge.-- the particle's mass and charge are always at the same place. It started as a "what else could electric current be?" other than the probability current. (Naturally you multiply the probability current by the particle's charge)

There are formal proofs, usually for relativistic QM, based on symmetries, Lorentz invariance -- spin plays a big role. Anyway, such efforts lead to the most general forms for a conserved current, and there's only one possible conserved current for any spin -- there can be a few wrinkles, which I've not mentioned. Most QFT and QED books will at least comment on this equality of currents.

Regards,
Reilly Atkinson
 

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