Generalized 6j symbols are defined in terms of orthonormalized Racah polynomials of a discrete variable and given explicitly as hypergeometric series. They extend the recoupling coefficients of ordinary angular moment-am algebra, including multiples of 1/4 as quantum numbers. A three-term recurrence relationship is exploited for extensive calculations and illustration of their properties. Their role is outlined as matrix elements for overlaps both between alternative spherical and hyperspherical harmonics and between alternative Sturmian sets, an important case being that of four-dimensional harmonics, which applies to the hydrogen atomic orbitals in momentum space.
Angular and hyperangular momentum momentum recoupling, harmonic superposition and Racah polynomials. A recursive algorithm
AQUILANTI, Vincenzo;CAVALLI, Simonetta;
2001
Abstract
Generalized 6j symbols are defined in terms of orthonormalized Racah polynomials of a discrete variable and given explicitly as hypergeometric series. They extend the recoupling coefficients of ordinary angular moment-am algebra, including multiples of 1/4 as quantum numbers. A three-term recurrence relationship is exploited for extensive calculations and illustration of their properties. Their role is outlined as matrix elements for overlaps both between alternative spherical and hyperspherical harmonics and between alternative Sturmian sets, an important case being that of four-dimensional harmonics, which applies to the hydrogen atomic orbitals in momentum space.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
