Wave function
A mathematical description of a quantum particle. The square of its size at a point gives the chance of finding the particle there.
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Analogy
A weather forecast: it gives odds, not certainties.
Example
probability density = |psi|^2Total over all space = 1
In practice
If the squared wave function is high at one spot, the electron is most likely found there.
Questions people ask
What does the wave function mean?
The wave function psi by itself is not directly measured. The square of its size at a point is the probability density of finding the particle there. Adding up this probability over all space must give exactly 1, since the particle must be somewhere.
What is Schrodinger's equation?
It is the equation that tells you how the wave function changes with time. Given the forces on a particle, you solve it to find the allowed energies and the chance of finding the particle in each place. It plays the same role for atoms that Newton's laws play for baseballs.