Atomic units Schrodinger equation written

In the case of hydrogen-1 ike atoms the Schrodinger equation can be written as (in atomic units) ... 

Calculations of the electronic structure of molecules, crystals and surfaces are often performed in atomic units. They are defined by setting the most important constants equal to unity h — eo — me — 1, where me is the electronic mass. The Coulomb law is written in electrostatic units V(r) = q/r, so that the time-independent Schrodinger equation for the hydrogen atom takes on the simple form ... 

If atomic units are used, the position-space Schrodinger equation can be written in the form ... 

We consider a closed-shell dimer AB with NA electrons and nA nuclei that can be assigned to the monomer A, and NB electrons and nB nuclei that can be assigned to the monomer B. The set of electronic coordinates r , = l,... NA + NB will be denoted by r, while the nuclear coordinates, Ry, y = 1,. ..nA + nB, will be denoted in short by R. The coordinates of electrons and nuclei are defined in a space-fixed frame. The nuclear masses will be denoted by My, and atomic units me = e = h= 1 will be used throughout this chapter. The Schrodinger equation for the total wave function Tf,ot can be written as,... 

Some authors who use atomic units use the customary symbols for physical quantities to represent the numerical values of quantities in the form (physical quantity)/(atomic unit), so that all quantities appear as pure numbers. Thus, for example, the Schrodinger equation for the hydrogen atom is written in SI in the form... 

The coordinates used to describe the helium atom are shown in Fig. 8.1. The Schrodinger equation, using atomic units and assuming infinite nuclear mass, can be written... 

To find the wave functions for an electron moving in one dimension, in the presence of two delta wells separated by the distance R(Fig. 5.10), write Schrodinger s equation. When written in atomic units,t it is... 

Stimulated by the wave theory of de Broglie, but well aware of the pitfalls and limitations of this theory, Erwin Schrodinger set up an equation for the hydrogen atom. The time-independent Schrodinger equation (SE) for a single electron and a nucleus with atomic number Z may be written using SI units and atomic units, respectively ... 

The time-independent Schrodinger equation (SE) for a diatomic molecule with N electrons and fixed nuclei A and B, with nuclear charges and Zg, respectively, may be written (atomic units) as... 

One method for solving the Schrodinger equation approximately for many electrons is density functional theory. In this theory (given in its practical form by the Kohn-Sham equations) one solves a single electron Schrodinger equation with an effective potential which depends on the total electron density. The one electron eigenvalue problem can be written (in atomic units) ... 

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