how cometh dept: ortho fns that dont cancel out

13.x.1430

in [Waerden]** §3 :

*
Lin transformation product with scalar product of two orthogonal functions.
o
<φ_j,Aψ_k> = A<φ_j,ψ_k>
*
The scalar product should be zero b/c the two functions φ,ψ are orthogonal
*
And yet van der Waerden states this is what gives the coeffs of A:
o
<φ_j,Aψ_k> = A<φ_j,ψ_k> = a_jk
*
¡¡¡ How Cometh ?!!¿؟?



** [waerden] = van der Waerden, Group theory and quantum mechanics , Springer 1974.
English translation of Die gruppentheoretische methode in der quantenmechanik , Berlin: Springer Verlag, 1932.


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