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To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication \\cite{sun2018} but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: $T_q|E_q|^{3/2}=\\frac{\\pi}{\\sqrt{2}} G\\left[\\frac{\\left(\\sum_{i=1}^N\\sum_{j=i+1}^Nm_im_j\\right)^3}{\\sum_{k=1}^N m_k}\\right]^{1/2}$. 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To be compatible with Semay's quantum n-body result, this letter reports a conjecture which had not be included in author's early publication \\cite{sun2018} but formulated in the author's research memo. The new conjecture for quantum N-body system is proposed as follows: $T_q|E_q|^{3/2}=\\frac{\\pi}{\\sqrt{2}} G\\left[\\frac{\\left(\\sum_{i=1}^N\\sum_{j=i+1}^Nm_im_j\\right)^3}{\\sum_{k=1}^N m_k}\\right]^{1/2}$. 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