Angular-Momentum and Spherical Tensor Operators

Y. F. Bow

K. T. Hecht

Ji Li

Using the method of nonlinear Lie algebra,the tensors of ladder operators are obtained.These tensors can shift the angular quantum numbers in ±2.Also the properties of the tensors' components and the relationships between angular momentum ladder operator vectors and the components are discussed in this paper.Thus, a conclusion is reached that the components of the 2 rank spherical noncancellation tensor operators are special linear combinations of the vector ladder operators' tensor products. They can shift the angular quantum numbers in 2 or-2,while the magnetic quantum numbers are changed in 0,±1,±2.

Gordon Baym

The addition theorem for spherical harmonics is just a special case of the law for the transformation of spherical harmonics under rotation of their arguments. Certain operators are scalars under rotation; this means that they commute with the total angular momentum and are unchanged by the transformation. The types of operators having simple transformation properties under rotation are known generally as tensor operators. The energy eigenstates of an atom, taking into account the spin-orbit interaction, are not usually eigenstates of the z component of the total orbital angular momentum, but are eigenstates of the total angular momentum, spin plus orbital. Sehwinger has looked at the theory of angular momentum from a point of view that enables one to carry out very elegant calculations of the various quantities occurring in the theory of angular momentum. The quanta of some different oscillators are simply the quarks that compose the strongly interacting particles.

Y. B. Band, Y. Avishai