Schrödinger equation on a generic radial grid

In this note, we discuss the choice of radial grid in numerical resolution Schroedinger equation. We detail transformation equation resulting from a change variable and function for generic grid, using either explicit or implicit form relation describing variable, apply it to $a r + b \ln(r)$ log-linear mesh. It is shown that, former case, first three derivatives Lambert $W$ are required. This complication becomes unnecessary if adopt instead.