In this problem, you will determine the formula for the Laplacian operator in spherical...

In this problem, you will determine the formula for the Laplacian operator in spherical coordinates.

(a) First, note that the cylindrical/spherical conversions given by formula (6) of §1.7 express the cylindrical coordinates z and r in terms of the spherical coordinates ρ and ? by equations of precisely the same form as those that express x and y in terms of the polar coordinates r and θ. Use this fact to write ∂/∂r in terms of ∂/∂ρ and ∂/∂?. (Also see formula (10) of this section.)

Formula 10

(b) Use the ideas and result of part (a) to establish the following formula: