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A method in atomic physics to simplify the Hamiltonian operator for many-electron atoms by assuming a radial and identical potential for all electrons. Learn the definition, reference and category of this approximation.
The central field approximation allows us to find solutions of the Schrödinger equation in terms of wave functions of the individual electrons: The zero-order Hamiltonian due to the central field will determine the gross structure of the energy levels specified by n , l .
Learn how the central-field approximation simplifies the Schrödinger equation for one-electron wave functions in many-electron atoms. Find out the meaning and application of the exclusion principle, which limits the number of electrons in each quantum state.
Apr 24, 2020 · In this so-called central-field approximation (CFA) , each electron is initially thought of as moving in a purely central potential, and having a wave function akin to hydrogenic electron orbitals. For an atom with many electrons, the zero-order approximation of its state will thus be a product of electron orbitals, whose occupation numbers ...
- Anders Kastberg
- 2020
Apr 28, 2020 · We call this the Central Field $U(r)$. Note it will not be a $1/r$ potential. We now write the Hamiltonian $$\hat{H}=\hat{H}_0+\hat{H}_1 \tag{24}$$ $$\text{where }\quad\hat{H}_0 =\sum_i\left\{-\frac{\hbar^2}{2m}\nabla_i^2+U(r_i)\right\} \tag{25}$$ $$\text{and }\quad\hat{H}_1 =\sum_{i>j}\frac{e^2}{4\pi\epsilon_0r_{ij}} -\sum_i\left\{\frac{Ze^2 ...
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Lecture 1. How we study atoms: emission and absorption of light. spectral lines. Atomic orders of magnitude. Basic structure of atoms. approximate electric field inside atoms. Atomic radiation. y. 1.
