Spherical Harmonics

We consider the Laplace equation in three dimensional space in spherical coordinates (the physics version of spherical coordinates). We had previously found the representation of the Laplacian in spherical coordinates ( • The Laplacian in Spher... ). We separate variables and show that the portions of the Laplace which depend on the angular longitude and latitude coordinates have solutions which are either trigonometric or associated Legendre functions ( • The Associated Legendr... ). The product of these two functions functions of longitude and latitude called spherical harmonics which arise in the study of the Schrodinger equation and other problems in mathematical physics.
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[@abbasibrahim9435]

I do not understand fully how to transform en equation from one coordinate system to another. Can you explain it geometrically?