In my efforts to write a Julia program that solves the time-dependent Schrodinger equation for helium, I’ve gotten as far as solving the time-independent case for the ground state, with some much-appreciated help from @kahliburke. I’m interested in exploring finite difference methods on a non-uniform grid, as this could allow me to overcome the FD methods’ limitation that increasing grid density in one region requires increasing it everywhere, with corresponding costs in terms of operator matrix size and iteration time. I’ve been attempting to locate Julia packages that will help me construct the second-derivative operator on a non-uniform grid and let me access it as a matrix. For example, MethodOfLines.jl seems to support such operator constructions, but only in the context of discretizing and solving the entire PDE. Due to the structure of the problem (detailed here, forgive me for not wanting to type out all that LaTeX again), I need to be able to access the 1D second derivative operator in order to build the full matrix operator to use with KrylovKit.jl 's eigsolve(), so packages that try to handle the full discretization+solution or wrap the operator in a special type won’t work. DiffEqOperators.jl seems promising, but it’s deprecated, so I’m wary of relying on it. CompactBases.jl promises to do what I want and then some, but it’s very unmaintained. FiniteDifferences.jl runs into the special type problem. With all the various differential equations packages in Julia, I suspect there’s something out there that does what I want, but I’m having a hard time finding it.