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Canonical transformations and matrix elements

par Quesne, Christiane ;Moshinsky, Marcos
Référence Journal of mathematical physics, 12, 8, page (1780-1783)
Publication Publié, 1971

Article révisé par les pairs

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Résumé :

We use the ideas on linear canonical transformations developed previously to calculate the matrix elements of the multipole operators between single-particle states in a three-dimensional oscillator potential. We characterize first the oscillator states in the chain of groups Sp(6) ⊃ Sp(2) X script O sign(3), Sp(2) ⊃ script O signs(2), and script O sign(3) ⊃ script O signL(2), and then expand the multipole operators in terms of irreducible tensors with respect to the Sp(2) X script O sign(3) group. Their matrix elements are obtained by applying the Wigner-Eckart theorem with respect to both the Sp(Z) and script O sign(3) groups. In this way an explicit expression for the radial integral of rk, k > 0, is obtained.