Potential step with E = V0; classically forbidden or allowed?

[hnicholls]

In describing a potential step where E = V0, with an interval 1 defined as x < 0 before the step and an interval 2 as x > 0 after the step, is the wave function in interval 2 classically allowed or classically forbidden, i.e. is it an oscillating function or a decaying exponential function?

 

[The_Duck]

Try solving the time-independent Schrodinger equation for the constant potential V(x)=V0 with E=V0. What do you get?

 

[hnicholls]

you get the ordinary differential equation

d^2/dx^2(y)=0

with solution

y=Ax+b

But, what I am interested in is solving this problem by defining the wave functions in the given intervals as either classically forbidden or classically allowed and then from those values determining the probability current densities for each interval and then the reflection and transmission percentages.

But to do this, I need to determine how to define interval 2 as CA or CF.