Theory of Angular Momentum

D, A. Varshalovich, A. N. Moskalev, and V, K. Khersonskii, Quantum theory of angular momentum. World Scientific, Singapore, 1988,... 

M. E, Rost, Elementary Theory of Angular Momentum, JohnWiley, Sons, Inc., New York, 1957. 

E. XT. Condon and G. H. Shortley, Theory of Atomic Spectra, Cambridge University Press, 1935 M. E. Bose, Elementary Theory of Angular Momentum, John Wiley and Sons, Inc., New York, 1957 A. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, 1957. 

Though these are alternative models, they are both particular cases of the non-adiabatic impact theory of angular momentum relaxation in gases. Thus, we prefer to call them models of weak and strong collisions , as is usually done in analogous problems [13, 33],... 

Varshalovich D. A., Moskalev A. N., Khersonski V. K. Quantum Theory of Angular Momentum (World Scientific, Singapore) (1986). [Kvantovaia teoria uglovogo momenta Leningrad, Nauka (1975)]. 

Figure 3-11. The shapes of the angular functions are determined only by the theory of angular momentum in spherical symmetry.

Term wavefunctions describe the behaviour of several electrons in a free ion coupled together by the electrostatic Coulomb interactions. The angular parts of term wavefunctions are determined by the theory of angular momentum as are the angular parts of one-electron wavefunctions. In particular, the angular distributions of the electron densities of many-electron wavefunctions are intimately related to those for orbitals with the same orbital angular momentum quantum number that is. 

The following books develop the quantum theory of angular momentum in more detail than this text. 

There are a variety of formalisms that allow for a mapping of a discrete quantum system onto a continuous analog (for reviews see Refs. 218 and 219). The most prominent examples are Schwinger s theory of angular momentum [98] and the Holstein-Primakoff transformation [97], both of which allow a continuous representation of spin degrees of freedom. To discuss these two theories, we consider a spin DoF that is described by the spin operators Si,S2,Si with commutation relations... 

Consider, furthermore, a (2i- - 1)-dimensional subspace of the Hilbert space with fixed 5. Then, according to Schwinger s theory of angular momentum [98], this discrete spin DoF can be represented by two bosonic oscillators described by creation and annihilation operators with commutation relations... 

In obvious analogy to Schwinger s theory of angular momentum, this N-level system can be represented by N oscillators, whereby the mapping relations for the operator and the basis states read [99]... 

Feenberg, E., and Fake, G. E., Notes on the Quantum Theory of Angular Momentum. Addison-Wesley, Cambridge, Mass., 1953. 

The elements of the theory of angular momentum and irreducible tensors presented in this chapter make a minimal set of formulas necessary when calculating the matrix elements of the operators of physical quantities for many-electron atoms and ions. They are equally suitable for both non-relativistic and relativistic approximations. More details on this issue may be found in the monographs [3, 4, 9, 11, 12, 14, 17]. 

A. P. Jucys and A. A. Bandzaitis. The Theory of Angular Momentum in Quantum Mechanics, Mintis Publishers, Vilnius, 1965 (in Russian, second extended edition in 1977). 

Varshalovich DA, Moskalev AN, Chersonskii VK (1975) Quantum Theory of Angular Momentum. Nauka, Leningrad (in Russian)... 

Secrest, D. (1975). Theory of angular momentum decoupling approximations for rotational transitions in scattering, J. Chem. Phys. 62, 710-719. 

In writing Eq. (2.6) the symmetry properties of the D-functions have been used, as presented in Appendix A (see (A. 11)). A detailed treatment of the properties of D-functions is considered in the quantum theory of angular momentum [379]. 

Re-examination of the first quantitative model of the atom, proposed by Bohr, reveals that this theory was abandoned before it had received the attention it deserved. It provided a natural explanation of the Balmer formula that firmly established number as a fundamental parameter in science, rationalized the interaction between radiation and matter, defined the unit of electronic magnetism and produced the fine-structure constant. These are not accidental achievements and in reworking the model it is shown, after all, to be compatible with the theory of angular momentum, on the basis of which it was first rejected with unbecoming haste. 

Elementary Theory of Angular Momentum, Kap. 3. New York J. Wiley Sons 1957. 

In both of the above treatments, spherical tensor and cartesian, we have factored the quadrupole interaction into the product of two terms, one of which operates only on functions of proton coordinates within the nucleus and the other only on functions of coordinates of electrons and protons outside the nucleus. We shall see in subsequent chapters that the spherical tensor form is rather more convenient for the calculation of matrix elements of 3Cq. However, we shall find this easier to appreciate once we have considered some of the theory of angular momentum in chapter 5 so we defer discussion until later. 

We recall from section 5.2.4 that, from the general theory of angular momentum, j can take half-integral (more strictly half-odd) values as well as integral ones. The particular case of j = 1 /2 deserves special mention because of its importance in the discussion of electron or proton spin. For j = 1/2, there are two possible states l/2, 1/2) and 11/2, -1/2) which are often denoted a) and /3) respectively. The spin operators which define these states are particularly simple. For example,... 

D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific Publications, Singapore and Teaneck, N.J., 1988. 

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