Quantum Mechanics by Daniel R. Bes

Author:Daniel R. Bes
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

This three-body problem may be reduced to a two-body problem by again considering a very massive nucleus. However, even the remaining problem is difficult to solve because of the presence of the Coulomb repulsion V between the two electrons. The total Hamiltonian is Ĥ0  + V, where

(8.13)

Here r12 =  | r1 − r2 | is the distance between the electrons.

We know how to solve the problem of two electrons moving independently of each other in the Coulomb potential of the He nucleus. Because the ground state energy of a hydrogen-like atom is proportional to Z2 and there are two electrons, the unperturbed energy is 8EH, where EH is the energy of the electron in the H atom. The antisymmetrized two-electron state vector of the ground state in the He atom is discussed in Sect. 7.2. Using this state, the first-order correction to the energy is (Sect. 8.7*)

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