Show eigenfunctions are orthogonal

[indie452]

hi

one of my past papers needs me to show that if 2 eigenfunctions, A and B, of an operator O possesses different eigenvalues, a and b, they must be orthogonal. assume eigenvalues are real.

we are given

$$\int A^*OB dx$$ = $$\int(OA)^*B dx$$

* indicates conjugate

 

[kuruman]

Can you write two eigenvalue equations, one for each eigenfunction? Also, please preview and write correctly your LateX equations before posting them, they will be easier to read.