Schrödinger's Cormorant

4.4 That’s a Super Position

When waves meet ...... the mathematics of constructive and destructive interference..

Waves do cool things. When you’re playing the bath, you no doubt create all kinds of interesting effects with them. We’re going to focus on just one of these because it’s going to turn out to be very relevant to where we are going: when waves meet they don’t generally ignore one another: instead they add together to make a composite wave. This is called superposition.

Sticking with simple sinusoidal waves, because we’re now ultra-confident with them, lets predict what happens when we add together two waves.

Case 1: you have two identical waves, travelling in the same direction and in-phase.

Question 4-4

Case 2: Now let’s consider two sine waves that are again identical and travelling in the same direction, but this time they are exactly out of phase, meaning that the peaks in one line up with the troughs in the other.

Question 4-5

These exercises justify mathematically the phenomena of constructive and destructive interference. You are probably already comfortable with these ideas – indeed we used them in chapter 1 – so the mathematical treatment may seem like a bit of an extravagance. However the point is that it shows that you can describe superposition just by adding up wave functions and this is an incredibly important idea in quantum mechanics.

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