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The functions ¢1(x) and ø2(x) are normalized:
d φ( (α) φι(α)
dx 0(x) 62(x)
= 1
= 1
-00
-00
and are mutually orthogonal
dx oi(x) $2(x)
dx 4i(x) $1(x) = 0 .
Is the function
b_(x) = ¢1(x) – $2(x)
normalized? If not, determine its normalization constant and write the formula for the
normalized y_ (x). Is the function
+(x) = ¢1(x) + ¢2(x)
%3D
orthogonal to _(x)?

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