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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orthogonal Eigenfunctions (Landau Lifshitz)

**Physics Forums | Science Articles, Homework Help, Discussion**