Probability Current Density or Flux

In summary: So, in a way, the probability flux is the particle velocity. Transmission coeff. is a measure of how well the wave packet is transmitting the momentum. And streams of particles are something that is only relevant in the Bohmian interpretation.
  • #1
manofphysics
41
0
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?
 
Physics news on Phys.org
  • #2
Anybody?
 
  • #3
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).
 
  • #4
manofphysics said:
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.
 

1. What is probability current density or flux?

Probability current density or flux is a concept in quantum mechanics that describes the flow of probability in a quantum system. It represents the rate at which the probability of finding a particle in a specific location changes over time.

2. How is probability current density or flux calculated?

The probability current density is calculated using the Schrödinger equation and the wave function of a quantum system. It is given by the product of the complex conjugate of the wave function and the gradient of the wave function.

3. What is the significance of probability current density or flux?

Probability current density or flux is a fundamental quantity in quantum mechanics that helps us understand the behavior of particles at the quantum level. It is used to study the flow of probability in a system and can provide insights into how particles move and interact with each other.

4. How does probability current density or flux relate to other quantum concepts?

Probability current density or flux is closely related to other quantum concepts such as wave functions, probability distributions, and quantum currents. It helps us understand the dynamics of quantum systems and can be used to calculate other important quantities, such as the expectation value of a particle's position.

5. Can probability current density or flux be measured?

While probability current density or flux cannot be directly measured, it can be inferred from other observable quantities such as the wave function or probability distribution. It is an important theoretical concept that helps us understand the behavior of particles at the quantum level.

Similar threads

Replies
1
Views
752
Replies
6
Views
880
Replies
1
Views
578
Replies
1
Views
848
Replies
4
Views
2K
  • Quantum Physics
Replies
1
Views
936
Replies
17
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
2K
Replies
2
Views
1K
Back
Top