In the framework of an explicitly correlated formulation of the electronic Schrödinger
equation known as the transcorrelated method, this work addresses some fundamental issues
concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases.
Focusing on the two-electron case, the integrability of mixed weak derivatives of
eigenfunctions of the modified problem and the improvement compared to the standard
formulation are discussed. Elements of a discretization of the eigenvalue problem based on
orthogonal wavelets are described, and possible choices of tensor product bases are
compared especially from an algorithmic point of view. The use of separable approximations
of potential terms for applying operators efficiently is studied in detail, and estimates
for the error due to this further approximation are given.