Unperturbed energy

The effeet of adding in the py orbitals is to polarize the 2s orbital along the y-axis. The amplitudes Cn are determined via the equations of perturbation theory developed below the ehange in the energy of the 2s orbital eaused by the applieation of the field is expressed in terms of the Cn eoeffieients and the (unperturbed) energies of the 2s and npy orbitals. 

The formulas for higher-order conections become increasingly complex. The main point, however, is that all corrections can be expressed in terms of matrix elements of the perturbation operator over the unperturbed wave functions, and the unperturbed energies. 

E s are the unperturbed energies of the electronic and vibrational states, respectively, and Bm is a constant energy factor which depends on the M excited state. It appears from Eq. (6.5) that ungerade symmetry of inverse energy mismatch between the relevant levels. 

If spin effects are neglected, the ground-state unperturbed energy level is non-degenerate and its first-order perturbation correction is given by equation (9.24) as... 

The next lowest unperturbed energy level however, is four-fold degenerate and, consequently, degenerate perturbation theory must be used to determine its perturbation corrections. For simplicity of notation, in the quantities and we drop the index n, which has the value... 

Numerical values of E > and E + for the helium atom (Z = 2) are given in Table 9.1 along with the exact value. The unperturbed energy value E l has a 37.7% error when compared with the exact value. This large inaccuracy is expected because the perturbation H in equation (9.80) is not small. When the first-order perturbation correction is included, the calculated energy has a 5.3% error, which is still large. 

If the transition is such that the unperturbed energy is strictly conserved (Ljba = 0) then from (9) it is seen that... 

Equation (1.24) expresses a simple but powerful physical idea, as illustrated (for = 2) in Fig. 1.3. This figure shows the unperturbed energy levels for a doubly... 

Since we are interested in dephasing, phases due to the (unperturbed) energy difference between the levels are immaterial. 

Notice that with the case 1 assumptions the energies after the interaction are raised and lowered by equal amounts, iAB, relative to the unperturbed energy, sA(=eB), and the resulting wave functions are an equal admixture of the unperturbed wave functions. 

Now consider perturbation theory for an unperturbed energy level that is n-fold degenerate, with the states... 

Fig. 1. Unperturbed energy levels of the organic molecules A and B in the separated atom limit and the corresponding perturbed energy levels of the bimolecular collision complex.

Equations (3.23) and (3.24) are valid also for a model space containing several unperturbed energies, e.g. several atomic configurations. These equations will form the basis for our many-body treatment. The generalized Bloch equation is exact and completely equivalent to the Schrodinger equation for the states considered. 

Figure 3. The total energy correction (full thick line) due to both the monopole (AEM dashed line), the pairing (AEp straight dashed line) and the quadrupole correlations (AEq dot-dashed line), for the Pb(z = 82) region. The unperturbed energy (upper straight dashed line) is also shown.

The Lamb shift is defined throughout the paper as a deviation from an unperturbed energy level1... 

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