Probability density of angular momenta distribution

In each case the probability density may be represented in spherical coordinates in the form of a three-dimensional diagram (see Fig. 2.2) in which the angles 0, ip correspond to the arguments of the function pb(0,ip), whilst the value of the function is plotted along the radius-vector r(0, ip). 

Let us now consider a few examples of probability density pb(0,ip). In cyclic coordinates, as used by us, the z-axis is a selected one see (A.l). It corresponds to the quantization axis in quantum mechanical 

A different situation arises in the absorption of linear polarized light causing P- or /2-type molecular transition. If the light is polarized along the 2-axis, we obtain, according to (2.8), the probability of light absorption as 

Finally, if the righthanded circular polarized light propagating along the 2-axis (E-1 = 1) produces an /2-type transition in the molecule, then the probability of absorption is 

In the investigation of the stereodynamics of chemical reactions, as dependent on the mutual orientation of the reagents, an important part, 

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Applying the latest model, the simplest equation for the probability density of angular momenta distribution in the absorbing state a may be written as follows ... 

Fig. 3.2. Isometric projection of the probability density of angular momenta distribution of ground (lower part) and excited (upper part) states (a) Q excitation (6) (P, R) excitation by light with E z.

In the case of righthanded circular polarized i -type excitation, when orientation of angular momenta takes place and the probability density of the angular momenta distribution is proportional to (1 — cos )2/2 (see (2.13)), only alignment of internuclear axes occurs, described by the probability density, which is proportional to (1/2)[1 + (sin20r)/2j. 

Three components (Q — —1,0,+1) of the multipole moment of rank K = 1 form the cyclic components of the vector. They are proportional to the mean value of the corresponding spherical functions (B.l) for angular momenta distribution in the state of the molecule as described by the probability density p 9,(p). These components of the multipole moments enable us to find the cyclic components of the angular momentum of the molecule ... 

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