Square-integrable

the special case for p=2 of p-integrable.

In mathematical analysis, a real- or complex-valued function of a real variable is square-integrable on an interval if the integral over that interval of the square of its absolute value is finite. The set of all measurable functions that are square-integrable forms a Hilbert space, the so-called L² space

This is especially useful in quantum mechanics as wave functions must be square integrable over all space if a physically possible solution is to be obtained from the theory.