My question is very specific. If my magnetic vector potential and electric scalar potential follow the lorenz gauge, then to find the gauge function that does the gauge transformation I have to solve the wave equation. For the wave equation do I have the freedom to solve the PDE for any coordinate system I want then convert after to necessary system or Let's say my magetic vector potential is in spherical coordinates would I need to solve the spherical wave equation. If I have to solve the spherical wave equation could you give an example of how to solve the spherical wave equation?

My question is very specific. If my magnetic vector potential and electric scalar potential follow the lorenz gauge, then to find the gauge function that does the gauge transformation I have to solve the wave equation. For the wave equation do I have the freedom to solve the PDE for any coordinate system I want then convert after to necessary system or Let's say my magetic vector potential is in spherical coordinates would I need to solve the spherical wave equation. If I have to solve the spherical wave equation could you give an example of how to solve the spherical wave equation?