Potential barrier. Schroedinger equation.

1. The problem statement, all variables and given/known data

Schroedinger equation for potential barrier.

What if #V_0=E##

First region. Particles are free.

##\psi_1(x)=Ae^{ikx}+Be^{-ikx}##

In third region

##\psi_3(x)=Ce^{ikx}##





2. Relevant equations

##\frac{d^2\psi}{dx^2}+\frac{2m}{\hbar^2}(V_0-E)\psi=0##

where ##V_0## is height of barrier.

For region II



3. The attempt at a solution

In second region

##\frac{d^2 \psi}{dx^2}=0##

from that

##\frac{d\psi}{dx}=C_1##

##\psi(x)=C_1x+C_2##

Boundary condition

##A+B=C_2##

##C_1a+C_2=Ce^{ika}##

##ikA-ikB=C_1##

##C_1=ikCe^{ika}##

System 4x4

Is this correct?

Could you tell me in this case do I have bond state?