Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

An Orthonormal Basis for a Function Space

Consider the space of functions of the form

Let's create an orthonormal basis for this space.

(a) First, demonstrate that the functions sin nθ form an orthonormal set; that is, prove that

(b) Next, find constants An such that if we define basis functions en = An sin(nθ) then

.

RETURNS

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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
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Email: redish@umd.edu

Last revision 28. October, 2005.