Hello people ! I have been studying Zettili's book of quantum mechanics and found that spherical harmonics are written <θφ|L,M>. Does this mean that |θφ> is a basis? What is more, is it complete and orthonormal basis in Hilbert? More evidence that it is a basis, in the photo i uploaded , in (5.163) it seems that he "opens" a complete basis to orthonormalization condition ... Furthermore, why does it have integrals of φ and θ ? I am confussed ... I have never heared about |θφ> basis ... (In expression |θφ> is it a product between θ and φ or should be a decimal point between them like in |L,M> ? ) I am asking because in potential wells we write the wave function like this <x|y> in position representation. So we use the |x> basis there. I want to know if i can treat |θφ> Like i treat |x> as a base. Thank you!