Abstract
Moshinsky has suggested a method of calculating Talmi transformation coefficients in which the coefficients with two radial quantum numbers equal to zero are calculated first and then recursion formulas over radial quantum numbers are applied. The coefficients with two radial quantum numbers equal to zero are shown to be expressed as factorials, in terms of a particular type of coefficient with all radial quantum numbers equal to zero, and a simple formula for these coefficients is given. Some interesting properties of the Moshinsky coefficient sums are found and a simple formula expressing the coefficients of the “three-body” hyperspherical function transformation in terms of generalized Moshinsky coefficients is obtained. Recursion formulas and symmetry relations for the Moshinsky coefficients are also discussed.
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