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Unformatted text preview: one translates to an integral statement, (3.2) (Here I am lazy and use the lower case where I have used before; this a standard practice in QM.) Since probabilities are always positive, we require . Now let us try to look at some aspects of classical waves, and see whether they can help us to guess how to derive a probability density from a wave equation. The standard example of a classical wave is the motion of a string. Typically a string can move up and down, and the standard solution to the wave equation (3.3) can be positive as well as negative. Actually the square of the wave function is a possible choice for the probability (this is proportional to the intensity for radiation). Now let us try to argue what wave equation describes the quantum analog of classical mechanics, i.e., quantum mechanics. The starting point is a propagating wave. In standard wave problems this is given by a plane wave, i.e.,...
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- Fall '10