Probability flux inside the finite potential barrier

[Haynes Kwon]

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?

 

[PeroK]

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?