Quantum Theory

Download Advanced Quantum Mechanics by Professor Dr. Franz Schwabl (auth.) PDF

By Professor Dr. Franz Schwabl (auth.)

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2c) Ix-x'l represent the kinetic energy of an electron, the potential feIt by an electron due to the nucleus, and the Coulomb repulsion between two electrons, respectively. Although the Hartree and the Hartree-Fock approximations have already been discussed in Sect. 3 of QM 111 , we will present he re a derivation ofthe Hartree-Fock equations within the second quantization formalism. This method is easier to follow than that using Slater determinants. 3) ar Here, 10) is the vacuum state containing no electrons and is the creation operator for the state li) == l

1b, where one must sum over all intermediate states. 2 Fourier Transformation of the Density The other operators considered in the previous section can also be expressed in the momentum representation. As an important example, we shall look at the density operator. 10) We have thus found the Fourier transform of the density operator in the momentum representation. 3 The Inclusion of Spin U p until now, we have not explicitly considered the spin. One can think of it as being included in the previous formulas as part of the spatial degree of freedom x.

I... ,ni, ... ) = (1 - ni)( _1)2 L j

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