Is the Schrodinger Equation easier to solve in Spherical Coordinates when dealing with the Hydrogen Atom?

Question

Recently, I have been researching the Schrodinger Equation. I am now attempting to derive the solution to the equation for the Hydrogen Atoms potential energy function. What I am wondering is that whether it is easier to do a coordinate change in the Schrodinger equation to make it Spherical. I am specifically working with this version: $${ih}\frac{\partial\psi}{\partial t}=[\frac{-h^2}{2m}\nabla^2+V(\mathbf r, t)]\psi$$ Additionally, I am wondering if there are any Spherical Harmonics you could pull out of this. Thanks in advance.