Radial kinetic energy

As the kinetic energy operator has no off-diagonal elements in the space-fixed axis representation we may more easily correct for the fact that the analysis line is not tmly in the asymptotic region as far as the centrifugal representation is concerned. We do this first by subtracting the residual centrifugal repulsion, I I + l)/(2p / ), from the radial kinetic energy at the analysis line in the product channel. Thus we use the expression... 

It is useful to keep in mind these three embodiments of the derivatives that enter into the radial kinetic energy in various contexts it will be useful to employ various of these. 

The presence of radial nodes also indicates that the electron has radial kinetic energy. The 3s orbital with 2 radial nodes has more radial kinetic energy than does the 3p which, in turn, has more than the 3d. On the other hand, the 3d orbital has the most angular energy... 

This arbitrariness was noticed by Cohen and Heine and by Schlosser28 who suggested that one way of resolving the difficulty would be to place extra conditions on the pseudopotential operator. In particular they proposed that the eigenfunctions xm should be required to have the minimum possible radial kinetic energy ... 

Another aspect of applications which should be noted is the fact that up to the present, calculations have been carried out for systems using Cartesian-type distance variables. Thus, in the calculations of atom-rigid rotor scattering (50), the first derivative in the radial kinetic energy was eliminated by the usual substitution... 

The first few radial wavefunctions for hydrogen are listed in Table 6.1 and the way in which R and R vary with distance from the nucleus is shown in Figure 6.4. The number of nodes (points where the wavefunc-tion crosses the r axis) is equal to n - I - 1. The radial kinetic energy is related to the curvature of the wavefunction and increases with the number of nodes. 

The radial kinetic energy of the electron also beconnes negative at large distances from the nucleus where, owing to tunnelling, there is still a finite probability of finding it. 

In the axial direction the recoil force is many orders of magnitude larger than the axial dipole force. The potential minimum with respect to the radial dipole force is E ot — —5 x 10 eV. In order to trap atoms in this minimum their radial kinetic energy must be smaller than 5 x 10 eV, which corresponds to the temperature T 5 x 10 K. 

Ve//(r) = 0. However, at smaller values of r, where Veffir) > 0, some of the initial kinetic energy is converted into energy associated with the effective potential. The distance of closest approach, or turning point, ft.p., is reached when the magnitude of the effective potential is equal to the initial radial kinetic energy, and the radial velocity becomes zero ... 

The non-interacting radial kinetic energy density for the ith excited state... 

The radial kinetic energy terms Radial grids and Fourier transforms... 

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