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## Main Question or Discussion Point

I've been reading QM by Landau Lifgarbagez, in which I've come across a statement I can't seem to get my head around.

It states (just before equation 3.6):

a_n = SUM a_m. INTEGRAL f_m. f_n. dq

( a_n is the nth coefficient, f_m is the mth eigenfunction of an operator, dq is the differential element.

It follows from the equation for determining the coefficients in a wavefunction composed of a linear sum of eigenfunctions of an operator:

a_n = INTEGRAL f_n. f. dq )

It then states that it is evident from this that the eigenfunctions must be orthogonal. I don't see how this is? I would like to understand this, as it would imply that orthogonality of eigenfunctions would fall directly out of the mathematics of QM!

It states (just before equation 3.6):

a_n = SUM a_m. INTEGRAL f_m. f_n. dq

( a_n is the nth coefficient, f_m is the mth eigenfunction of an operator, dq is the differential element.

It follows from the equation for determining the coefficients in a wavefunction composed of a linear sum of eigenfunctions of an operator:

a_n = INTEGRAL f_n. f. dq )

It then states that it is evident from this that the eigenfunctions must be orthogonal. I don't see how this is? I would like to understand this, as it would imply that orthogonality of eigenfunctions would fall directly out of the mathematics of QM!