By V. Devanathan

A direction in angular momentum strategies is vital for quantitative learn of difficulties in atomic physics, molecular physics, nuclear physics and sturdy nation physics. This ebook has grown out of this sort of direction given to the scholars of the M. Sc. and M. Phil. measure classes on the college of Madras. An effortless wisdom of quantum mechanics is a vital pre-requisite to adopt this direction yet no wisdom of team conception is believed at the a part of the readers. even if the subject material has group-theoretic beginning, precise efforts were made to prevent the gro- theoretical language yet position emphasis at the algebraic formalism dev- oped via Racah (1942a, 1942b, 1943, 1951). How some distance i'm winning during this venture is left to the discerning reader to pass judgement on. After the booklet of the 2 vintage books, one by means of Rose and the opposite through Edmonds in this topic within the yr 1957, the applying of angular momentum ideas to unravel actual difficulties has turn into so universal that it truly is came upon fascinating to prepare a separate path in this topic to the scholars of physics. it truly is to cater to the wishes of such scholars and learn staff that this booklet is written. a good number of questions and difficulties given on the finish of every bankruptcy will allow the reader to have a clearer realizing of the topic.

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There are in vogue different conventions2 for the definition of D functions. The convention that is used here is identical with the convention of Rose (1957) and is widely used in elementary particle physics. For instance, Jacob and Wick (1959) use this convention in the formulation of helicity formalism3 for the description of scattering theory. 5. 1, the spherical components of a spherical tensor of rank 2 are explicitly given in terms of the spherical components of two vectors A and B. Since we know how the spherical components of a vector transform, it is a straight-forward procedure to construct the rotation matrices D2 ( α,β, γ ) for the transformation of a spherical tensor of rank 2.

10) This transformation can be expressed more elegantly in the matrix form as follows. 11) ROTATION MATRICES - I 37 The equations for transformation of the spherical components can be obtained following the same procedure as before. 17) Lastly, we have to perform a rotation through an angle γ about the Z2 axis. The resulting transformation matrix is the product of the three transformation matrices obtained for rotations through the three Euler angles. 4. The Rotation Matrix D1(α,β,γ ) It is to be pointed out that the transformation matrix M is not the rotation matrix defined in this book.

41) 48 CHAPTER 5 For a vector located at the origin, these two rotation will invert the vector. But it is not so in the case of spinors. However, it can be shown that the two spinors ϕ and ϕ ' differ by a rotation through an angle π about the Z-axis. 43) That is why a spinor can be considered as a vector with a thickness. 4. The Clebsch-Gordan Series In this section, we shall obtain a coupling rule for rotation matrices and it is deduced from the coupling scheme of two angular momenta. 45) where the argument ω of the D matrix stands for the set of Euler angles α,β,γ.