What is the physical interpretation of the imaginary component in the spherical harmonics? I am under the impression that when we sketch the shapes of the spherical harmonics we exclude the imaginary components.
Consider it a price to be payed in order to keep the theory consistent. As already stated, for pure states phase factors are factorized through.When we take the modulus squared of the spherical harmonics we loose the term containing the azimuth angle and the imaginary number. Isn't this a problem since we loose information about the shapes?