Integrals for Lower Bounds to the Exact Energy
explicitly correlated Gaussian
energia alsókorlát
explicit korrelált Gauss-függvény
Absztrakt:
The analytical solutions to quantum few-body systems are rarely found meaning that, for atoms
and molecules, stationary states are found by numerical computations. If high precision is required
then the computations can be expensive and, in contrast to experiment, it can be difficult to attach
rigorous error bounds to results. The exact energy of quantum states can be estimated using the
variational method which provides an upper bound to the exact energy. Achieving lower bounds of
comparable quality to upper bounds would then provide an energy range within which the exact
energy eigenvalue would reside. The formal theory of lower bounds is well established, but the
numerical application to systems occurs less frequently compared to that of upper bounds.
