Which video processing software can be used to merge two videos of the same view recorded by two separate cameras?

After Effects has a difference matte tool that might be of use to you, but this would involve two views from the same camera position - i.e time adjustments as your teacher walks in and out of frame. Or you could capture a still from your locked camera position, use that for a difference matte, and then use the matte to key in a second camera very close to your main camera but just covering a closeuop of your blackboard. It would not be automatic - it would take setting up and rendering - but you could probably get an acceptable results this way. I've successfully used difference matte to put two people in place at the same time, when they never were, without anyone spottting the insert - kind of like bluescreen without the blue screen. Just make sure the camera is locked and steady on the tripod, no moves, no autoiris or autofocus. The Adobe website will offer you more on AE.

Eugenia's answer is 100% correct.  Let me give you a 50% correct answer, which is a poor-man's way you could rig this: Assuming you're only concerned about what is written on the chalkboard: First create a 2D transform for both channels to eliminate perspective on the chalkboard.  Next, create masks (or pair of mask) that create a seamless chalkboard image no matter which half of the board comes from which channel.  You'll need some overlap in the middle. With the board lit, but no teacher, adjust the black level of each video channel OR record the average density of the empty chalkboard images.  Now, add the teacher. You can now switch between your two inputs for the two halves of the board based on where the teacher isn't.  The way you can do this is to low-pass filter (median) the channels and compare it to either black or the stored density (depending on which method you chose).  Which ever partition the teacher is in, you choose the mask that places the other camera's video in that segment of the output.  (The tools I used to use - Shake and Media Illusion -  had a scriptable switch node that could do this.  I would guess Nuke could do it.) Problems you're going to need to deal with: When the teacher is close to the board (like writing), the board is likely to be occluded from both cameras' FOV.  The teacher is going to cast a shadow on the board. There will be an area in front of the board where the teacher may be visible in both cameras, but the left-side on one and the right-side on the other (as the teacher steps away from the board).

You could try to merge the two videos vertically left/right with the break some where between the combined region.I would think a video splicer could do that for you. At that point the when the teacher is writing on the board they will would be blocking the point of view of both cameras. I would think an overhead wide angle lens would be better. What is the end result you are looking for? One solution is a tablet/projector.. seems like the best solution to me. I know some faculty that love the journal on windows tablet and post the files online.