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What is a wavefunction?

What is a wavefunction? Here are some definitions.

Noun
  1. (physics) A mathematical function that describes the propagation of the quantum mechanical wave associated with a particle (or system of particles), related to the probability of finding the particle in a particular region of space.
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The results can be used to define the kilogram in terms of the Planck constant that relates the frequency of a particle's wavefunction to its energy.
The interpretation of the wavefunction was one of the thorny issues facing the early pioneers of quantum theory.
Spartan, the chemistry computational software package released by Wavefunction, Inc.
They describe modern wavefunction or density functional technology as translated into familiar chemical language through natural bond orbital analysis.
That is to say, the wavefunction is antisymmetric under exchange of two particles.
The transition rate depends on the overlap between the ground state wavefunction for a low energy collision and the excited bound state wavefunction.

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