Momentum operator
In quantum mechanics, momentum is an operator which maps the wave function ψ(x, t) to another function. If this new function is a constant p multiplied by the original wave function ψ, then p is the eigenvalue of the momentum operator, and ψ is the eigenfunction of the momentum operator. In quantum mechanics, the set of eigenvalues of an operator are the possible results measured in an experiment. The momentum operator is an example of a differential operator, for the case of one particle in one dimension, the definition is
where ħ is Planck's reduced constant, i the imaginary unit, and partial derivatives (denoted by ) are used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator. The "application" of the operator on the wave function is as follows:
It is usual to think of the p-operator as "multiplying" the function, but this is not what is happening. The derivative of the function is taken.
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.
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