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?
The probability flux inside a finite potential barrier refers to the flow of probability through the barrier, which represents the likelihood of a particle passing through the barrier at a given energy level.
Probability flux is calculated using the Schrödinger equation, which takes into account the wave function of the particle and the potential barrier. The flux is then determined by taking the product of the probability density and the velocity of the particle.
The probability flux is affected by the energy level of the particle, the width and height of the potential barrier, and the shape of the barrier. Additionally, the mass and charge of the particle also play a role in determining the probability flux.
As the energy of the particle increases, the probability flux also increases. This is because higher energy particles have a greater chance of overcoming the potential barrier and passing through it. However, at very high energies, the probability flux may start to decrease due to the wave function of the particle spreading out and decreasing the likelihood of passing through the barrier.
The probability flux inside a finite potential barrier is significant because it helps us understand the behavior of quantum particles in confined spaces. It also has practical applications in fields such as quantum computing and tunneling microscopy.