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Born rule
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Probability from the wavefunction.
The probability of finding a particle in a region is ∫|ψ|²dx; for general measurement, probability of eigenvalue a is |⟨a|ψ⟩|².
|ψ|² = 0.2 at x means a 20% density per unit length.
Probabilities are fundamental, not due to ignorance, in standard QM.
In more detail
The Born rule states that the probability of finding a particle in a region is the integral of |ψ|² over that region. It links the wavefunction to measurable outcomes.
Real-world uses
- Physicists compute measurement probabilities using the Born rule.
- Quantum chemists predict reaction probabilities this way.
- Quantum chemists use the Born rule to calculate the probability that a molecule is found in a particular configuration.
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Frequently asked questions
Why use the square?
The squared magnitude is always positive, which is needed for probabilities.
Does the rule work for all measurements?
Yes, for any observable with the appropriate operator.
What does the Born rule say?
The probability of finding a system at a point is the squared magnitude of its wavefunction at that point.
Related topics in Quantum Mechanics
Heisenberg uncertainty principle · Energy–time uncertainty · Wavefunction · Normalisation · Schrödinger equation (time-dependent) · Schrödinger equation (time-independent)