Abstract
We study in an algebraic manner the symmetric basis of the Calogero model and the non-symmetric basis of the corresponding Calogero model with distinguishable particles. The Rodrigues formulas are presented for the polynomial parts of both bases. The square norm of the non-symmetric basis is evaluated. Symmetrization of the non-symmetric basis reproduces the symmetric basis and enables us to calculate its square norm.
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Wadati, M., Nishino, A., Ujino, H. et al. Symmetric and Non-Symmetric Bases of Quantum Integrable Particle Systems with Long-Range Interactions. Journal of Statistical Physics 102, 1049–1064 (2001). https://doi.org/10.1023/A:1004875625099
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DOI: https://doi.org/10.1023/A:1004875625099