# Orthogonal bases for $L^2(0,1)$

I would like to understand whether $$\left\lbrace \sin (n\pi x) \, e^{-\sqrt{a-(n\pi)^2}x}\right\rbrace$$ for $$a>0$$, is an orthogonal bases for $$L^2(0,1)$$. Do you have any smart idea how to proceed, or maybe is there any useful known result?

Sorry, I just realized it is clear it cannot be... just by considering the inner product between two of them with different index $$n$$...