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
L
2
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.
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