ISSN:
1572-8897
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Chemie und Pharmazie
,
Mathematik
Notizen:
Abstract A new class of half-integer rank spherical tensors is introduced. The motivation for investigating this new class of tensors originated from a desire to be able to partition matrices using mixtures of fictitious integer and half-integer spin labels. However, it is shown that they can also be used as annihilation/creation operators for spin-1/2, 3/2, etc., particles. In particular, half-integer rank tensors can be used to add/subtract a spin-1/2 particle from a given ensemble. Thus they can be viewed as the natural generalization of the raising and lowering operatorsI ±, in that they change bothI andM, simultaneously. The concept of a “universal rotator” is introduced and it is demonstrated that half-integer rank tensors obey the same contractional and rotational properties as their integer counterparts, but with half-integer rank. In addition, it is shown that half-integer rank tensors can be used to factorize the Pauli spin matrices. Finally, an example of the use of half-integer rank tensors in the block-diagonalization of a simple 3 x 3 matrix is presented and discussed.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01277571
