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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!

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# Spherical harmonics and basis

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