Probability amplitude
Complex number whose square modulus gives probability density.
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square modulus of this quantity at a point in space represents a probability density at that point.
- field
- Quantum mechanics
- known_for
- Probability amplitude, Born rule, Born probability
- proposed_by
- Max Born
- associated_interpretation
- Copenhagen interpretation
Lore & Background
The interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. Properties of the space of wave functions were used to make physical predictions, such as emissions from atoms being at certain discrete energies, before any physical interpretation of a particular function was offered.
Reader's Guide
Probability amplitudes are central to quantum mechanics, linking the abstract quantum state to observable measurement outcomes. Under the Copenhagen interpretation, when a measurement is made, the system jumps to one of the eigenstates of the observable, with probability proportional to the absolute square of the corresponding probability amplitude. This relationship, the Born rule, requires that the sum of these probabilities equals 1, a normalization condition. The concept was vigorously contested at the time by original physicists such as Schrödinger and Einstein, and remains a source of philosophical difficulties and debate. Mathematically, a probability amplitude is often represented as a wave function belonging to the L2 space of square integrable functions, with its absolute square serving as a probability density function. The formalism extends to continuous amplitudes, where the probability density is defined as the Radon–Nikodym derivative with respect to the Lebesgue measure. The behavior of probability amplitudes under sequential measurements of non-commuting observables leads to the characteristic uncertainty and probabilistic nature of quantum mechanics.
Did You Know?
- The square modulus of a probability amplitude at a point in space represents a probability density at that point.
- The probabilistic concepts were vigorously contested by Schrödinger and Einstein.
Frequently Asked Questions
Who is Probability amplitude?
Probability amplitude is a complex number assigned to a quantum system that encodes how the system behaves. Its square modulus at any given point in space yields the probability density for finding the particle there.
What are Probability amplitude's powers/role?
It serves as the mathematical bridge connecting a system's quantum state to the outcomes an observer actually measures. Without it, there would be no way to translate the abstract wavefunction into concrete prediction probabilities.
How does Probability amplitude's story end?
It doesn't really end—it remains a core ingredient of the Copenhagen interpretation and standard quantum mechanics to this day. Every calculation of measurement likelihood in modern QM still runs through amplitudes and their squared magnitudes.
More in Quantum Mechanics And Foundations 1-18
Spotted an error? Know more?
This is a living reference — every entry is fact-audited, and reader corrections feed straight into our audit queue. Suggest an edit · See this site's audit record