I Is the Laplacian Operator Different in Radial Coordinates?

[SeM]

Hi, I have that the Laplacian operator for three dimensions of two orders,

\nabla ^2 is:

1/r* d^2/dr^2 (r) + 1/r^2( 1/sin phi d/d phi sin phi d/d phi + 1/sin^2 phi * d^2/d theta^2)

Can this operator be used for a radial system, where r and phi are still valid, but theta absent, by setting theta = 0 ?

so giving:1/r* d^2/dr^2 (r) + 1/r^2( 1/sin phi d/d phi sin phi d/d phi) ?

Does that make sense or is the Laplacian operator of second order in radial (polar) coordinates different?

Thanks

 

[Orodruin]

https://en.wikipedia.org/wiki/Laplace_operator#Two_dimensions