Born rule ↩

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aliases: [Born's rule]
created: 2021-12-11 01:10:04
modified: 2022-01-16 14:29:35

In quantum mechanics, we have probabilities of measuring different values of an observable. These probabilities are described by the Born rule.

For position

In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is the following:

So the probability of finding it in a region in space is the following:

This of course only makes sense if the wave function is normalized:

So is a unit vector in Hilbert space.

For discrete spectrum

The Born rule states that if an observable corresponding to a self-adjoint operator with discrete spectrum is measured in a system with normalized wave function , then