Probability current versus electric current

In summary, the probability current density and electric current density are different in quantum mechanics. While the former is dependent on position and obeys the continuity equation, the latter is not and is determined by the particle's charge. However, they are considered to be the same thing in most cases, with the exception of some coupling constants and symmetries in relativistic QM. This understanding is essential in many applications of QM, such as in the study of ionization or neutral particles like neutrons and neutrinos.
  • #1
BeauGeste
49
0
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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  • #2
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.
 
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  • #3
thanks. that helps.
 
  • #4
You could have a probability current when dealing with an electrically neutral body. So, no, they're not really the same thing.
 
  • #5
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?
 
  • #6
I meant to say you can have a probability current when doing quantum mechanics with uncharged objects like neutrons or neutrinos.
 
  • #7
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
 

1. What is probability current?

Probability current is a concept in quantum mechanics that describes the flow of probability density. It represents the rate at which the probability of finding a particle at a certain position changes over time.

2. What is electric current?

Electric current is the flow of electric charge through a conductive material. It is measured in amperes (A) and is caused by the movement of electrons or ions within the material.

3. How are probability current and electric current related?

Probability current and electric current are related through the continuity equation in quantum mechanics. This equation states that the total probability current must be conserved, meaning that any change in the probability density must be accounted for by a corresponding change in the electric current.

4. How is probability current different from electric current?

The main difference between probability current and electric current is the quantity that is being measured. Probability current measures the flow of probability density, while electric current measures the flow of electric charge. Additionally, probability current is a concept in quantum mechanics, while electric current is a concept in classical physics.

5. What are the applications of probability current and electric current?

Probability current and electric current have various applications in different fields of science and technology. Probability current is important in understanding the behavior of particles at the quantum level, while electric current is crucial in the functioning of electronic devices and power systems. They both play a crucial role in fields such as quantum computing, electronics, and energy generation and distribution.

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