Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation (Q2838587)

The author describes a molecular system using the Schrödinger equation NEWLINE\[NEWLINE -\frac{1}{2}\Delta u + V_{ne}u + \frac{1}{|x-y|} u = \lambda u NEWLINE\]NEWLINE in the space \( H^{1,1}(\mathbb R^{3},2)\). For the system of \(n\) electrons in the stationary case, this equation is reduced in the space of functions defined on the domain \(\mathbb R^{3}\times ({-\frac{1}{2},\frac{1}{2}})\). The Galerkin method, using an orthogonal basis of wavelets, is applied to solve this eigenvalue problem. An estimate of the error is given for the potential term of a one-electron system and for a two-electron operator.