Abstract
The quantum model of a cluster, consisting of A identical particles, coupled by the internal pair interactions and affected by the external field of a target, is considered. A symbolic-numerical algorithm for generating \(A\!\!-\!\!1\)-dimensional oscillator eigenfunctions, symmetric or antisymmetric with respect to permutations of A identical particles in the new symmetrized coordinates, is formulated and implemented using the MAPLE computer algebra system. Examples of generating the symmetrized coordinate representation for \(A\!\!-\!\!1\) dimensional oscillator functions in one-dimensional Euclidean space are analyzed. The approach is aimed at solving the problem of tunnelling the clusters, consisting of several identical particles, through repulsive potential barriers of a target.
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Gusev, A. et al. (2013). Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_14
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DOI: https://doi.org/10.1007/978-3-319-02297-0_14
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