Rotations et Moments Angulaires en Mecanique Quantique - Rotations and angular moments in quantum mechanics - IN2P3 - Institut national de physique nucléaire et de physique des particules Access content directly
Journal Articles Annales de Physique Year : 2001

Rotations et Moments Angulaires en Mecanique Quantique - Rotations and angular moments in quantum mechanics

Abstract

As in classical mechanics, rotation in quantum mechanics is a transformation which deals with angular momentum. The difference with classical mechanics comes from the fact that angular momentum is a vector operator and not a usual vector and its components do not commute. As for any transformation in quantum mechanics, to each rotation we can associate an operator which acts in state space. The expression of this operator depends on whether the rotation is passive, that is we do a rotation of the coordinate axes and the physical system is left unchanged, or active, in which case the coordinate axes are unchanged and the rotation is performed on the physical system. In the first part (Chaps. 1 and 2) of this book, details concerning both aspects are given. Following the definition of the geometrical transformation associated with the most general rotation, we give the expression of the rotation operator for specific cases. Transformation laws for scalar fields, vector fields and spinor fields are given as well as transformation laws for scalar operators, vector operators and more generally, for operators of any rank. The second part (Chaps. 3 and 4) deals with angular momentum algebra. We define the coupling coefficients of 2, 3 and 4 angular momenta as well as the recoupling coefficients. The definition of the irreductible tensor operator, which is a generalisation of scalar and vector operators, is given as well as the Wigner-Eckart theorem. The application of this theorem to more complex cases is studied.
Fichier principal
Vignette du fichier
19832.pdf (1.12 Mo) Télécharger le fichier

Dates and versions

in2p3-00019832 , version 1 (18-09-2006)

Identifiers

  • HAL Id : in2p3-00019832 , version 1

Cite

J. van de Wiele. Rotations et Moments Angulaires en Mecanique Quantique - Rotations and angular moments in quantum mechanics. Annales de Physique, 2001, 26, pp.1-169. ⟨in2p3-00019832⟩
41 View
890 Download

Share

Gmail Mastodon Facebook X LinkedIn More