Orthonormality of cosine eigenfunctions in the infinite square well

[Cogswell]

So in the infinite square well, the eigenfunctions are $\psi_n (x) = \sqrt{\dfrac{2}{a}} \sin \left( \dfrac{n \pi}{a} x \right)$

Each state is orthogonal to each other, and so $\displaystyle \int \psi_m (x) ^* \psi_n (x) dx = \delta_{mn}$

Does this also hold if they were cosines?

 

[VantagePoint72]

Yes, the cosines are also orthonormal.

 

[Bill_K]

You should be able to easily prove this yourself. Just use the trig identity for cos A cos B, and do the integral.