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| :''the special case for p=2 of ].'' | :''the special case for p=2 of ].'' | ||
| In ], a ] or ]-valued function of a real variable is '''square-integrable''' on an interval if the ] over that interval of the square of its absolute value is finite. The set of all ]s that are square-integrable forms a ], the so-called ] | In ], a ] or ]-valued ] of a real variable is '''square-integrable''' on an ] if the ] over that interval of the square of its ] is ]. The set of all ]s that are square-integrable forms a ], the so-called ] | ||
| This is especially useful in ] as ] must be square integrable over all space if a physically possible solution is to be obtained from the theory. | This is especially useful in ] as ] must be square integrable over all space if a physically possible solution is to be obtained from the theory. | ||
Revision as of 14:56, 17 April 2005
- 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 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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