Probability flux inside the finite potential barrier

Click For Summary
SUMMARY

The discussion focuses on the calculation of probability flux inside a finite potential barrier, as described in the Bransden textbook. It is established that the probability current density remains constant for one-dimensional stationary states, with verified constant flux outside the barrier. However, the probability current density inside the barrier is not provided in the textbook, leading to confusion among readers. The main inquiry is how to derive the probability flux within the barrier, indicating a gap in the provided information.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically stationary states.
  • Familiarity with the concept of probability current density.
  • Knowledge of finite potential barriers in quantum mechanics.
  • Basic algebra and calculus skills for solving quantum equations.
NEXT STEPS
  • Review the derivation of probability current density in quantum mechanics.
  • Study the mathematical treatment of finite potential barriers in quantum systems.
  • Learn about the continuity equation in quantum mechanics.
  • Explore advanced topics in quantum mechanics, such as wave functions and their properties.
USEFUL FOR

Students and professionals in quantum mechanics, physicists working with potential barriers, and anyone seeking to deepen their understanding of probability flux in quantum systems.

Haynes Kwon
Gold Member
Messages
21
Reaction score
0
In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current density inside the barrier. I tried to find the flux but I couldn't figure it out yet. How do you find the probability flux inside the barrier?
 
Physics news on Phys.org
Haynes Kwon said:
In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current density inside the barrier. I tried to find the flux but I couldn't figure it out yet. How do you find the probability flux inside the barrier?

Are you asking what the formula is or did the algebra get too difficult?

Generally on PF we ask you to post the solution as far as you can. How far have you got with this?
 

Similar threads

Undergrad Can an electron quantum tunnel inside the potential barrier?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Tunneling through a finite potential barrier
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Potential step and tunneling effect
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad A particle measured in a too high potential
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Why Can Electrons Tunnel Through Barriers in Quantum Mechanics?
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Transmission: Finite Potential Barriers & Potential Steps
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Tunneling from Rectangular barrier - Exponential Decay ?
  • · Replies 5 ·
Replies
5
Views
3K
E<V Potential Step Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Graduate A particle locked inside an arrangement of Dirac delta potentials
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad I want to understand how the transmission coefficient is obtained
  • · Replies 3 ·
Replies
3
Views
1K