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Wavefunction
Intermediate
Complex function whose squared magnitude is probability density.
P = ∣ψ∣²The state of a quantum system is described by a complex wavefunction ψ(x, t); |ψ|² gives the probability density of finding the particle at x. Phase information gives interference.
Hydrogen 1s ψ ∝ e^{−r/a₀}.
ψ itself isn't directly observable.
In more detail
The wavefunction ψ describes the state of a quantum system. Its squared magnitude gives the probability density of finding the particle at a given place.
Real-world uses
- Chemists compute molecular orbitals from wavefunctions.
- Quantum computing uses wavefunctions of qubits.
- Physicists compute the probability of finding an electron in a region of an atom using the wavefunction.
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Frequently asked questions
Is the wavefunction physical?
It is a mathematical description, but it determines measurable probabilities.
Is it real or complex?
In general it is complex, and only the magnitude squared is directly measured.
Is the wavefunction a physical wave?
It is a mathematical function that describes the state of the system, and its squared magnitude gives probabilities.
Related topics in Quantum Mechanics
Double slit with electrons · Heisenberg uncertainty principle · Energy–time uncertainty · Born rule · Normalisation · Schrödinger equation (time-dependent)