Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Angular-momentum integrals integral evaluation

In order to evaluate the matrix element in Eq. (4.151), (p S p0), we must calculate three-dimensional integrals. In the following we show, however, that the matrix element can be reduced to a sum over one-dimensional S -matrix elements. This is obtained via an expansion of the momentum eigenstates (R p) in a basis where we can use that the angular momentum of the relative motion is conserved. [Pg.98]

The evaluation of this integral by conventional methods (even for the special case m = m2 = m2 = 0 when the rotation matrices reduce to spherical harmonics) is extremely laborious. We shall use this result in the derivation of the Wigner-Eckart theorem and other angular momentum relationships later in this chapter. [Pg.158]

The integrals in Eqs. (149) and (150) can be evaluated as follows. We slightly deviate from a strictly classical analysis by quantizing the orbital angular momentum I and the diatom rotational angular momentum j. That is, we assign... [Pg.50]

The first step in reducing the MBPT expressions into a form suitable for numerical evaluation is a decomposition of the Coulomb integrals Uy w into sums of products of angular momentum coupling coefficients and radial integrals. To accomplish this decomposition, we first expand the kernel of the Coulomb integrals l/ri2 as... [Pg.138]

The generalized coordinate q and its conjugate momentum p vary periodically, and the line integral is evaluated over one cycle. (A similar quantization condition on angular momentum led to the famous Bohr postulate L = nh for the hydrogen atom in the old quantum theory [16].) For vibrational motion subject to a potential U K) in a diatomic, the classical energy is E = p llp -f- U R). The integral in (4.80) then translates into... [Pg.156]


See other pages where Angular-momentum integrals integral evaluation is mentioned: [Pg.93]    [Pg.441]    [Pg.163]    [Pg.234]    [Pg.275]    [Pg.153]    [Pg.314]    [Pg.161]    [Pg.191]    [Pg.705]    [Pg.410]    [Pg.26]    [Pg.27]    [Pg.28]    [Pg.30]    [Pg.76]    [Pg.270]    [Pg.270]    [Pg.271]    [Pg.171]    [Pg.264]    [Pg.304]    [Pg.236]    [Pg.499]    [Pg.191]    [Pg.126]    [Pg.441]    [Pg.117]    [Pg.118]    [Pg.124]    [Pg.280]    [Pg.193]    [Pg.144]    [Pg.125]    [Pg.201]    [Pg.178]    [Pg.91]    [Pg.263]    [Pg.527]    [Pg.208]    [Pg.248]    [Pg.186]    [Pg.202]    [Pg.253]   
See also in sourсe #XX -- [ Pg.348 ]




SEARCH



Angular integral

Angular momentum

Integral evaluation

© 2024 chempedia.info