Lecture III : The Many-Body Hamiltonian and the Functional Derivative
ثبت نشده
چکیده
• Electron-electron interaction : This is again a Coulombic interaction involving pairs of electrons. This part of the Hamiltonian is what makes the many-body problem so hard, in most cases impossible, to tackle. Almost all electronic structure calculation methods resort to approximations which simplify the electron-electron interaction. The quality of the particular calculation used for a system depends on how well this approximation is chosen.
منابع مشابه
Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos
This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملDetermination of Chromium(III) and Magnesium(II) Ions in Pharmacological and Real Water Samples using Potentiometric Sensors based on Chitosan Schiff base Derivative as Green and Sensitive Ionophore
In the study, novel and sensitive carbon paste electrodes (CPEs) developed for thepotentiometric measurement of Cr(III) and Mg(II) ions in pharmacological and water samples.CPEs as indicator electrodes were prepared from a mixture of four components, includinggraphite powder, paraffin oil, multi-walled carbon nanotubes (MWCNTs), and a greenionophore (Chitosan Schiff base...
متن کاملTopics in Enumerative Algebraic Geometry Lecture 12
Let the notation be as in the previous lecture. Let G be any complex semisimple Lie group unless otherwise specified. Let us recall that we are looking for the differential operators D1, · · · , Dr on the maximal torus which commute with the operator Q(q ∂ ∂q )−ΣQkkqk. Our approach will be to construct integrable system, called Toda lattice, with the Hamiltonian Q(q ∂ ∂q ) − ΣQkkqk. Then the op...
متن کاملExistence and continuous dependence for fractional neutral functional differential equations
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
متن کامل