Here is a part of what was posted in the link to which you refer:nathangrand said: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
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.
Continuity of function is a property of mathematical functions that describes the smoothness and connectedness of the graph. It means that there are no breaks or jumps in the graph and that the function can be drawn without lifting the pen from the paper.
Continuity of function is determined by three criteria: the function is defined at the point in question, the limit of the function exists at that point, and the limit equals the value of the function at that point. If all three criteria are met, the function is considered continuous at that point.
Continuity and differentiability are related but distinct properties of functions. Continuity means that there are no breaks or jumps in the graph, while differentiability means that the function has a well-defined derivative at that point. A function can be continuous but not differentiable, but if a function is differentiable, it must also be continuous.
Continuity of function is important in understanding the behavior of a function. If a function is continuous, it means that small changes in the input result in small changes in the output. This allows us to make predictions and analyze the behavior of a function with more accuracy.
Continuity of function is important in real-world applications because it allows us to model and analyze real-world phenomena with mathematical functions. These functions can then be used to make predictions, optimize processes, and solve problems in various fields such as physics, engineering, economics, and more.