Hydrogen-like atom perturbed

In order to obtain an approximate solution to eq. (1.9) we can take advantage of the fact that for large R and small rA, one basically deals with a hydrogen atom perturbed by a bare nucleus. This situation can be described by the hydrogen-like atomic orbital y100 located on atom A. Similarly, the case with large R and small rB can be described by y100 on atom B. Thus it is reasonable to choose a linear combination of the atomic orbitals f00 and f00 as our approximate wave function. Such a combination is called a molecular orbital (MO) and is written as... 

Perturbation Theory for a Hydrogen-like Atom Confined Within an Impenetrable Spherical Cavity... 

Table 7 Perturbation theory coefficients E for expansion of the energies in powers of R for the Is, 2p, 3d, 4f and 5g levels of a hydrogen-like atom confined in a spherical box of radius R (see Equation (51) of text). The numbers in parentheses indicate the power of 10... 

Unfortunately, the stationary Schrodinger equation (1.13) can be solved exactly only for a small number of quantum mechanical systems (hydrogen atom or hydrogen-like ions, etc.). For many-electron systems (which we shall be dealing with, as a rule, in this book) one has to utilize approximate methods, allowing one to find more or less accurate wave functions. Usually these methods are based on various versions of perturbation theory, which reduces the many-body problem to a single-particle one, in fact, to some effective one-electron atom. 

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