Construction of a complete orthogonal system for the quantum-mechanical three-body problem

Microscopic cluster description of12C

“…The symmetrical Hyperspherical Harmonics basis for a three-particle system was realized many years ago (see, e.g., [43,44]). An explicit form of a few basis functions for small values of the total angular momentum (L = 0, 1 and 2) can be derived.…”

Construction of Hyperspherical Functions Symmetrized with Respect to the Orthogonal and the Symmetric Groups

“…[14], proves the computational advantage of the present algorithm. In Table I we compare the total number of hscfps and of ohscfps for 4-body hyperspherical functions, i.e., hyperspherical functions of three Jacobi coordinates, where the values of K 3 , the hyperspherical angular momentum, are 4,6,8,10. From this table we see that the number of ohscfps is reduced drastically in comparison with the number of hscfps as the value of K 3 is increasing.…”

“…Actually, there are some more restrictions on the possible values of the parameters * j, k in (3) and (4). For polynomial representations [26] all these values must be integers.…”

“…The method of hyperspherical harmonics, introduced in 1935 by Zernike and Brinkman [1] and reintroduced in the 60's by Delves [2] Simonov [3] Zickendraht [4] and Smith [5] has revealed itself in the last two decades as a powerful tool for the study of few-body systems. The hyperspherical functions were applied to atomic three and four-body systems like the He 6 Li atoms [6,7,8] to nuclear systems like the triton and the : particle [9,10] and even to hadronic calculations [11].…”

The group theoretical description of the three-body problem

“…Another possibility of constructing a basis was demonstrated by Zickendraht,39 however the used method is also too complicated and does not give a sufficiently general result.…”