given the wave function F(x) for a matter wave the probability of finding the particle is given by F^2...how is this explained? in my text book its given as according to Bohr's postulate. i have been doing quantum mechanics for a term now and i always took this for granted!!
Technically, the probability of finding the particle between x and x+dx is |F(x)|<sup>2</sup> dx |F(x)|<sup>2</sup> is a probability density, not a probability in itself. How is this explained? Well, consider light waves as an analogy. Suppose we take two electric fields E1 and E2 to represent two light waves. The intensity of each wave is |E|<sup>2</sup>, and the intensity is what we measure when, for example, we project the light on a screen. If we allow the two waves to interfere, the result is E = E1 + E2. Now for the interesting part. The resulting intensity is: |E|<sup>2</sup> = |E1|<sup>2</sup> + |E2|<sup>2</sup> + 2(E1*)(E2) Note that it is NOT just |E1|<sup>2</sup> + |E2|<sup>2</sup>. If we're going to represent quantum states of light as waves, we need the same kind of algebra, so we denote the probability that a photon is measured at a particular location as given above.
Hi ecclesiastes, Just to add a bit of history, it was actually Max Born who proposed the probabilistic interpretation of the wavefunction that is now commonplace. The rule that probabilities correspond to the square of the wavefunction as James described above is called the Born rule.
