What is Continuity of Function and How Does it Lead to A+B=C?

[nathangrand]

In this post: https://www.physicsforums.com/showthread.php?t=230996

..continuity of the function is described. I don't understand what this means but know that it leads to A+B=C

Can someone offer an explanation as to what continuity is and why it leads to this

 

[SammyS]

In this post: https://www.physicsforums.com/showthread.php?t=230996

..continuity of the function is described. I don't understand what this means but know that it leads to A+B=C

Can someone offer an explanation as to what continuity is and why it leads to this

Here is a part of what was posted in the link to which you refer:

analyzing the simple-step scattering problem for E<V, we find that the solution to the schroedinger equation is:

PHI(left) = Aexp(ikx)+Bexp(-ikx)
PHI(right) = Cexp(-qx)

Continuity of the function and it's derivative at x=0 gives the relations between the parameters A, B and C.

The function, Φ(x), is continuous at x=0 provided that:

lim_(x→0^‒)Φ(x) = Φ(0) = lim_(x→0⁺)Φ(x).​

This gives A + B = C = Φ(0)
The derivative is continuous if a similar relationship holds for it.

This gives: A ‒ B = -qC/(ik)

 

[nathangrand]

Thanks I get it now!