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momentum operator
In quantum mechanics, momentum (like all other physical variables) is defined as an operator, which "acts on" or pre-multiplies the wave function to extract the momentum eigenvalue from the wave function: the momentum vector a particle would have when measured in an experiment. The momentum operator is an example of a differential operator.
At the time quantum mechanics was developed in the 1920s, the momentum operator was found by many theoretical physicists, including Niels Bohr, Arnold Sommerfeld, Erwin Schrödinger, and Eugene Wigner.
==Origin from De Broglie plane waves==
The momentum and energy operators can be constructed in the following way.〔''Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles'' (2nd Edition), R. Resnick, R. Eisberg, John Wiley & Sons, 1985, ISBN 978-0-471-87373-0〕
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