The calculation of the terms of the optical spectrum of an atom with one series electron
1932; Royal Society; Volume: 138; Issue: 836 Linguagem: Inglês
10.1098/rspa.1932.0203
ISSN2053-9150
Autores Tópico(s)Advanced Physical and Chemical Molecular Interactions
Resumo1. The theoretical determination of the energies of the stationary states of an atomic system is bound up with the solution of the many-body problem— in particular, with the determination of wave functions of many-electron atoms. An exact solution is not known, but approximations to it have been made by Hartree, Slater, Fock and Lennard-Jones.§ The method adopted is to replace the physical problem by an artificial one which admits of a solution, e. g., Hartree replaces the actual many-body problem by a one-body problem with a central field for each electron. Generally, the Schrodinger equation for an atom of nuclear charge N is { N Ʃ i = 1 (-1/2∇ i 2 -N/ r i ) + N Ʃ i > j = 1/ r ij -E} Ψ = 0, using atomic units11 and the usual notation. The artificial system replacing (1.1) has the equation { N Ʃ i = 1 (-1/2∇ i 2 - v i ) -E} ψ = 0, V i being a function of the co-ordinates of the i th. electron only. Equation (1.2) is separable, and reduces to equations of the type {-1/2∇ i 2 - v i ) -E i } ψ = 0, in the space co-ordinates of the - i th electron alone. If the solutions of equations (1. 3) are Ψ(α∣1), Ψ(π|p), where the Greek letter is the label of the wave function, and the numeral or Roman letter indicates the electron whose co-ordinates are substituted, then a solution of (1. 2) is ψ = Ψ(α∣1) Ψ (β∣2)....Ψ(π|p). The form of wave function which must be assumed in order to satisfy Pauli’s Exclusion Principle and be antisymmetric in the co-ordinates of all pairs of electrons, is the determinantal form Ψ = ∣ψ = Ψ(α∣1) Ψ (α∣2)....Ψ(α| p ) ∣ ∣ψ = Ψ(β∣1) Ψ (β∣2)....Ψ(β| p ) ∣ .................................................. ∣ψ = Ψ(π∣1) Ψ (π∣2)....Ψ(π| p ) ∣ which is the sum of the expressions obtained by permuting the co-ordinates 1, 2,........., p in the product (1. 4) and taking account of the signs of the permutations. Thus we obtain an approximate wave function for the whole atom in terms of the one-electron wave functions.
Referência(s)