- #1

Isaac0427

Gold Member

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##\int \phi_1^*\phi_2dx=\int e^{-ix}e^{2ix}dx=0##

Why is this?

I understand how orthogonality would work with dirac deltas (i.e. I know why position eigenfunctions are orthogonal in position space and why momentum eigenfunctions are orthogonal in momentum space, etc.) but I am unclear of how it works with plane waves.

Also, I am specifically asking why ##\int e^{-ix}e^{2ix}dx=0##, not why orthogonality works in general (I understand its derivation using the definition of hermitian operators and the inner product).