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Two quantum quartic anharmonic many-body oscillators are introduced. One ofthem is the celebrated Calogero model (rational $A_n$ model) modified byquartic anharmonic two-body interactions which support the same symmetry as theCalogero model. Another model is the three-body Wolfes model (rational $G_2$model) with quartic anharmonic interaction added which has the same symmetry asthe Wolfes model. Both models are studied in the framework of algebraicperturbation theory and by the variational method.Comment: 17 pages, LaTeX, 1 figur

QUARTIC ANHARMONIC MANY-BODY OSCILLATOR