6533b7d8fe1ef96bd126978c
RESEARCH PRODUCT
Tensor Operators and the Wigner-Eckart Theorem
Jouni Suhonensubject
Tensor contractionPhysicsWigner–Eckart theoremCartesian tensorSymmetric tensorTensorTensor densityTensor operatorMathematical physicsTensor fielddescription
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant and contains the physics of the matrix element.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-01 |